Dear John,
Yes, going for a degree whilst or prior of the flight training is a smart move. You must do that, a lot of pilots work on that or try to set a business or have another job to get back if aviation doesn't work.
Depending on your age, I would go for a degree if you are young enough and the go for aviation. If you are on thirties, then you are on hurry if you want to start a career on aviation. Ageism discrimination is true whatever anyone will say, things are that for example some carriers state during their hiring process: "experience commensurate with age", that means that if you are 30 and 1000 TT you are in a bad position to make it.
Also consider the financial part very seriously, don't
your life for aviation because there's any guarantee that anyone will find a job on the airlines 100% sure. So if you can pay your trianing without debt, then it's whole different status to start your career than if you take a lon that you will have to pay-back at a ratio of 500/1000 USD a month.
PM if you need any advise!
Good luck!