I'm not sure about uprights, but concert grands can (reportedly) reach 110 decibels at the position of the person playing it - in a small room. A large upright is not nearly as loud, but even if it's only half the volume of a grand, it could still reach 100+ dB.
OSHA allows for 85 dB for 8 hours. Every 3 dB over that, the time is cut in half. So:
88 dB - 4 hours
91 dB - 2 hours
94 dB - 1 hour
97 dB - 30 mins
100 dB - 15 mins
103 dB - 7.5 mins
So I'd guess it's possible to damage your hearing with an upright piano, depending on your endurance to play at constant fortissimo or above for relatively long periods? To me, it seems unlikely, since the dynamics in most music doesn't stay at ff for long periods at a stretch. Then again, you might find yourself deliberately practising a ff passage for a long period of time and be in the danger zone?
My practice room is well treated with acoustic panels and such, as I hate small-room acoustics and prefer it somewhat dead. But I have a friend whose upright is in an small untreated room with hardwood floors and it's nearly unbearable at ff. Definitely causes a *cringe* reaction in me.