It would certainly be stressful, but it shouldn't be life-threatening. First off, if you have housemates, make sure you ok everything with them first, parrots are adorable, but they are loud, and it wouldn't be fair to your housemates to force them to live alongside your parrots if they can't handle it.
If you're able to, speak with your parrot's vet about what to do, because they're going to be much more knowledgeable than a random stranger on the internet. And will be able to give much better advice.
When I transported my parrot (budgie) in the past, it worked out fine, we just made sure the cage wouldn't rattle and shake too much, and we secured it in place with the seatbelt, though that wasn't for a full 2 hour trip. Talking with them or having the radio on the whole way should help keep them calm, they won't be happy, but they'll manage. Probably goes without saying, but avoid sudden stops and sharp turns.
Also, TIL that Americans call budgies "parakeets."