In some cases, you would be very wrong.
[ETA caveat: What I (truepenny) say in this post is the result and reflection of my own academic Pilgrim's Progress, in my particular department, with the particular professors I studied under. What I describe is only one strand of literary scholarship; as angevin2 points out in the comments, other departments and other programs are different. So don't take me as gospel, please, except on my own experience.]
truepenny: I am the product of very conventional, tradition-minded undergraduate and post-graduate programs. This means that, although New Criticism is no longer fashionable, and although a great deal of energy is expended in explaining earnestly how we don't do that anymore, the fact of the matter is, it is what we do. My prelims list (the required texts for the exams to achieve dissertator status), in common with every other prelims list in my department, was exclusively primary texts. There was a little note at the top (the academic equivalent of the fine print) saying that of course the student would supplement the list with critical and historical reading, yada yada, but you could get by perfectly well--as I in fact did--by doing no more secondary reading than was assigned in your various classes.
So my knowledge of the literature is fairly encyclopedic--although there are gaps where my coursework failed to be supplemented by my prelims reading. (The other thing to understand about the prelims list, which is seven pages long, is that nobody reads all of it. You can't.) Drayton is one such gap, Burton another, and in general my knowledge of Henrician literature is pretty darn spotty. Except for Wyatt, whom I adore in that wouldn't-want-to-meet-him sort of way. And I can talk about the period in literary terms, talk about genre and tradition and who was being influenced by whom and why Hero and Leander is such a clever and subversive thing to do and why Jonson and Webster in particular felt a need for such posturing prologues to their printed plays.
But my knowledge of history and culture is patchy, and what I know about the lives of the poets and playwrights, I've learned, almost entirely, from Bear. Because, academically, I was trained by people who were trained by New Criticism, and there's still a feeling that biographical details are sordid and petty and we should have our minds on higher matters. You study aspects of the culture, as they relate to the literary text you want to discuss, but you don't get down and wallow in it and read everything you can find about it and learn it. Because New Criticism says the literary text is paramount, and when the chips are down, that's still what the American university system is teaching.
matociquala: This was my experience in college too. And I must say, my knowledge of the literature and my general education are incredibly spotty compared to truepenny's. She has a classics background; I have Bullfinch's Mythology. She reads a bit of Latin and Greek. I have less of either than Ben Jonson's famous contumely would have alloted Shakespeare. I regularly mispronounce common English words. She doesn't.
I haven't read half, or a third, or a quarter of the period literature that she has. I have four years of college but no degree, and though I was majoring in English Lit and Anthropology before a joint problem with money and a brush with death, or rather deconstructionism, scared me clean out of academia, my concentration was not renaissance literature.
In fact, I didn't get bitten by the bug until 2002, when a chance conversation with an Oxfordian gave me the idea for the book that would eventually turn into The Stratford Man.
Only having learned the literature in the past, when I started reading history and biographies, I realized I had a totally skewed idea of how Renaissance theatre worked. These were not poets scribbling in ivory towers. These were men who fought and duelled and stole each other's wives, and shared the same stages, the same financial problems, the same work tables--sometimes the same work--and the same rented beds. Their plays were as often veiled assaults on one another as not--when they weren't assaulting each other physically--and the romanticized view of Art for Art's sake didn't hold water. They were social pariahs and outcasts, struggling artists, and they often died young and hard.
Ben Jonson the hard-drinking womanizer who pistol-whipped Marston with his own gun is a very different man than Ben Jonson the jealous classicist and unofficial Poet Laureate, who had an uneasy and envious relationship with Master Shakespeare. And yet they're both the same man.
truepenny: Whereas I know the facts of the Elizabethan/Jacobean theatrical system (Discuss Rosencrantz and Guildenstern's London theatrical gossip in Act II, scene ii, of Hamlet, with special emphasis on the "little eyases." Use the back of the page if necessary.), but in a weird way, with no context. Because in the academic setting you study Shakespeare. And Marlowe. Oh, and Jonson because post-modernism makes him trendy. And maybe Middleton and Rowley's Changeling. And The Duchess of Malfi. If you read other playwrights, odds are good you will be taught them only in comparison to Shakespeare ("X is doing this, which Shakespeare does much better in ..."). But not in context with Shakespeare. You study them in isolation. You aren't encouraged to think about the fact that Shakespeare and Marlowe, Shakespeare and Jonson, knew each other. Collaboration is acknowledged (and if you're very lucky and get a very good professor, you may get to read a Beaumont and Fletcher play), but the plays you read and talk about are the solo ventures, the ones that fit our post-Romantic view of Art and the Artist. You read for text first--and in fact, academics go out of our way to erase the poet from our discussions.
This is in part actually appropriate and necessary. (It felt like I spent half my time last semester when I was teaching intro Shakespeare saying, "We don't know what Shakespeare wanted us to learn from A Midsummer Night's Dream--if anything at all. Don't try to talk about the author's intentions, because you can't know them.") But in part, I think, it's the effect of canonization, of pigeon-holing, of building little boxes to put literary texts in. And human beings are messy and perverse and don't fit in the boxes we build for ourselves.
Which is what I think the autodidactic approach teaches and the academic approach does not. It's a cliché to say that academics, in their ivory tower, are out of touch with humanity and real life, and in fact, academics as people are every bit as real and human and Machiavellian--Hobbesian, even--as anyone else. But we tidy up our subjects of study. Post-modernism, as a theory, and deconstructionism have a bad rep, but their initial impulse was to try to talk about the messiness of literature. Then they got trendy and codified and we're right back where we started with the text pinned on our dissecting tray like an unfortunate frog.
Academia is not holistic. And that's what I admire about matociquala's scholarship, the way she understands that everything fits together.