Hi - I know you posted this 2 days ago, but I've been in a similar situation in terms of being quite academic and doing a creative arts course.
I did my foundation at Chelsea, and while the combined CCW course will probably be a bit different, I personally found that the course did have some elements of academia involved but not really a tremendous amount. We had to do 'contextual studies' in addition to all the practical projects, and this involved lectures, seminars and essays including a general run through of art history. Lots of room for discussion and debate in the seminars I found, and broadly, everything we covered was to push our own practice as artists/designers in a modern context as opposed to a proper in depth analysis of other people's work.
It was all really interesting, but it was only once a week or once every few weeks, so not a lot, and it was not enormously challenging for anyone who can write reasonably well and enjoys discussion. Also, something which I found quite good (I don't know if they'll do it again this year, but it would be amazing if they did), we had a cinema programme thing, where we'd watch really 'artsy' films in a cinema in Leicester Sq once a week. For free. Again, lots of talking and an essay on one of the films was required.
I should think the CCW course will be similar to Chelsea's individual one, just in a different setting and loads more students.
At degree level, you definitely get lectures and a handful of essays, but again, it's predominantly practical. In terms of research and so on, obviously, you'll have to undertake some within the context of your projects and to inform your work, but it's less 'taught', I imagine. I know at Chelsea, where I'm doing graphic design in septemeber, there's a whole lot of 'professional practice' lectures from working designers and stuff. And within UAL, there's always lectures and talks on a broad range of art and design subjects outside of college hours which usually anyone can attend, and often featuring big names within the industry.
But yeah. You kind of have to do some of the leg work yourself if you want to further your knowledge as well as practical skills, but it's an art school, so they were never going to offer side courses on Maths. However, if you decide to do your degree at a university which offers other non creative subjects you may be able to take electives in academic stuff too.
Sorry for being so long - this is like an essay!