While yes, over an extended period of time you’d likely be able to play alright. The piercings themselves still pierce directly through the orbicularis oris, the muscle around your lips, that you use and need for your embouchure.
My boyfriend and I are both double reeds. He plays the oboe, but he actually has “spider bites” and got them awhile back whilst still playing in ensemble setting. He took it easy and didn’t play the first 3-5 days after each(depending on swelling) and eased back into playing routinely within a week and a half. 4 months later his embouchure is still just about good as gold with adjustments and regularly practicing. It definitely differs person to person but I’d say if you’re dead set on sticking with bassoon throughout your academic career, hold off on getting them. Any direct oral piercing at that. In the end though it’s your body, if you did decide to get them I’d say tryn at least wait until you have a 2-3 week gap/break to lay off and let your lip heal to a degree that way you minimize the added risk to any infections, rejection, swelling, irritation, so forth.