I have 2 horses with a bit of a sway back, my old guy Blue I've had for 13 years and it's never caused him a problem, he's in his mid-late 30's now so I've retired him but he would still go if I asked him to.
This is him
My other one is Legacy, I've had him for a year and a half, he does him some soreness but I don't think it's due to his sway back. He is stiff in the neck most of all. I believe his soreness is due to years of incorrect tack and bad riders although I can't be sure because he's an auction horse and I have no history on him, the vet put him about the same age as your horse.