Yes, you can carbonate with just the co2 from the tank, no priming, no fuss, no mess. Most of us do it in this manner.
Kegs can be stored at room temp with no carbonation for long periods of time with two caveats. First, your sanitation must be good. Second, you should purge the oxygen from the headspace by hooking up the co2 and opening the relief valve for a few seconds. This leaves a nice blanket of co2 on top of your beer.
I have always just force carbed at serving temp and pressure for about a week with good results. I had a friend over and was anxious for him to try an Arrogant Bastard clone. It had only been in the fridge for about 24 hours, so was still flatter than a platter of pi$$. I pulled it out, kicked up the pressure to 30 psi, laid the keg over at about a 45 deg angle and shook the bejesus out of it until I heard the co2 slow down. I readjusted my pressure, put the keg back in the fridge and forgot it for about an hour. I purged the excess pressure and it poured real nice.
Me like beer.