Yes, perfectly safe.
It is just a little annoying when it comes to engine start (no compressed air available directly) and air conditioning in very hot conditions (the ground supplied air is usually rubbish) or when there is no ground conditioned air available.
To start the engines without the APU we would get the groundcrew to hook up a unit that supplies us with high pressure air. We use this to start an engine, then push back, rev the running engine a bit and use 'bleed air' from the running engine to start the other engine (talking A320, I'm sure it applies to most jets).