Definitely do the degree.
That said, if there are sponsorships going, don't stop applying just because you're at uni. Quite a few of the people I've met at sponsorship selections were still undergraduates.
And I'd agree with P T Flea that it may well be worth just signing up for the 3 year course. There's nothing worse than being stuck where you don't want to be. This would also give you two years earning at graduate rates (rather than undergraduate - read minimum wage - rates) in case you don't get sponsored and you have to pay for it all yourself.