In short, yes you can.
Best not to try to downshift without the clutch, it's just unhealthy, definitely for the bike, and quite possibly for you.
Clutchless upshifts are fine though, no damage and relatively simple but if you're a new rider I'd say save it for the track.
I say do it after 2nd gear only. 1st to 2nd is a stretch and will likely tear some shit up if not executed properly. But from 2nd gear and up just put pressure on the shifter upwards and left of the gas ever so quickly and it should fall right in.