Sounds like a reasonable enough plan. The selection and the training are rigourous so a back up plan of a useful degree might be a good idea in case you don't make it.
I applied after my degree,despite still having no idea what I wanted to do in life. There was a NATS recruitment advert on the back of a magazine in the career adviser's waiting room! That was 15 years ago and I haven't looked back. It's a great job.