Using LC oscillator to create square wave AC
if it could it possible.

Yes. since these mosfets are essentially voltage-controlled, of course you can control them with a voltage oscillator.
You'll want to make sure that the transition from &quot;completely off&quot; to &quot;completely on&quot; is fast, or else you'll have half-on MOSFETs for a long duration, which will get very hot.
Your LC-Oscillator won't work like that (you need some way to get power in there, otherwise the thing will not oscillate), but I'm sure you can find enough oscillator circuits on wikipedia.