Think I am going to get flamed for this
oh dear lol
Oh well here goes, in my opinion you shouldn't base every decision you have to make in life on whether it will help or not you becoming an airline pilot. Each airline is an employer, there isn't a set rule on what is an airline pilot and you don't need to all complete the same degree, go to the same uni etc and appear to them like you have just got off the wannabe tread mill. Different employers look for different characteristics and if one airline doesn't think you are suitable to them, another may well think you are the ideal candidate.
If you take a gap year make sure you utilise it, earn some money to pay for Uni and enjoy, or gain extra skills such as a language. There is no point in taking a gap year to squander it by lying in bed all day etc. Secondly the important decision is whether you, at the present time have had enough of education and therefore feel a year away will recharge the batteries and allow you to prosper at University when you finally get there.
Oh and for the record there is no set rule that you have to complete your degree to apply to British Airways sponsorship or any other. You can apply whilst you are there, and drop out or if you are ending your course negotiate to finish Uni and then start training if you are successful.
Wish you all the best in whatever you choose, just make sure you look at the wider picture.
Sagey