I get hard too easily. I got an erection the other day talking to a female coworker face to face because I could see her cleavage! I don't think she noticed the hard on, but DID notice me staring at her tits and smiled.
I see lots of guys on cam start out limp and get hard quickly with no touching. Other times it gets hard by the time they get their pants totally off.
So yes, I would say its very common for men to get erect without touching.