Is it safe to touch the ground contact?
Well, in theory, assuming wiring is done right the ground prong will contact the ground terminal in the outlet and that terminal is connected to the ground with a thick enough wire and touching it is as safe as touching a washer or fridge chassis.

However you should not do that ever, because Murphy is out there...

First of all, the ground prong is very close to the phase and neutral prongs and there's a slim yet quite real chance that you will touch the phase prong at the same time. Once this happens you get a ground fault and if there's no ground fault protection that yields a major short circuit which gets you a nice several millimeters deep burn on your finger (I have nice experience touching phase and neutral terminals together with the same finger - heals in two weeks and can be fatal in an unlucky electrical setup). If you're really unlucky (like you're touching a grounded appliance at the same time) you get a ground fault through your body and this yields fatal shock. Such things do happen - it's just a matter of time. You do that no-problem one thousand times, then you accidentally do it wrong and consequences are dire. Chances are slim, but quite real and potential consequences are serious.

Second, you can't be sure at all times each outlet is wired right. Wiring may fail at some point and put you at risk. You can also try to do that in other person's house where wiring happens to be done wrong and that puts you at risk.

Finally, there's this cheater plug thing. Clearly if you plug a three-pronged device into a cheater plug and then try to plug the cheater plug and habitually try to find the prong you likely find either phase or neutral prong and that puts you at risk.

So the bottom line is you technically can do that, but you really should not - getting such habit is potentially very dangerous.