My dad has two schwinn bicycles that have been hanging upsidedown from hooks for around 15 years (without use, so sad). I pulled one of these bikes down (to see if the size fit, it didn't). Everything was in excellent condition, minus the dust and cracked sidewalls on the tire. Hanging hadn't caused any issues.

I have all my bikes are hanging from hooks placed in the rafters. I alternate directions so I can get more in a smaller space. I put them towards the back of the garage so when I park the car/truck there, the bikes hang over the hood but will not hit the cab.