Yeah, it's mostly possible. Just expect to take worse losses than you would with some manual intervention, and take some time in the simulator to work out what does and doesn't jive well with autopilot AI. There's some setups that do pretty well with humans (just about anything involving high speed, or mixed long/short ranged weapon loadouts), that the AI humps the idiot ball over.
I do a bit of both, most of the time. Don't mind letting autopilot handle a lot, and the AI controlled stuff usually does a decent job of staying alive,* but sometimes you just have to take the wheel to get the ruddy ship to actually engage, instead of flap around the outskirts of a fight with their thumb wedged in their nethers, venting CR and time into space.
Officers definitely help a lot, though. You often want to do a lot of fighting just get them more XP, so you can nudge 'em in the direction of whatever sort of ship you want them piloting.
All that said, you can also set yourself up in a support role instead of trying to dogfight. Get in a carrier, load yourself out with missiles and PD/long range weapons, that sort of them. Fix up your ship so you don't have to aim or move all that much, heh. Lots of autofire on a heavy ship can manage something similar.
*Sometimes it does rather more than that, actually. I've had a time or two I was off chasing a wolf or kite or somethin', then came back to one of my larger ships soloing a multiple or two in tonnage worth of enemies.