You could always drop out if you got accepted, if you thought that was the best thing to do..
Without wanting to start (yet another) debate on here about whether a degree is worthwhile if you're planning a career in ATC - you have to consider that just because you get through the selection doesn't mean you have a job for life. So if you start your degree, get the job, quit the degree, come to the college.. there are many many points at which you can still fall down and whilst it's usual to get a second chance, it's not a guarantee. And then you'd be a bit stuck. Of course you could reapply to Uni again, but you might have a big wait before starting again.
All depends where your priorities lie and what you think is best for you. If you want to make a go of it as soon as possible then do. If you're a bit more wary and want a little more security, I would suggest finishing the degree first and then applying might be the better route.
IMVHO. YMMV. IANAL.
Having said all that, I am jealous of the guys who are at the same stage as me at Heathrow who aren't even 20 yet!
(To answer the question, some people on our course went from stage 1 to starting job within 3 weeks. Others (like me) took 6 months)