Yes, AH aircraft catch fire without major structural failure. I've never seen one go out though, even if the punctured fuel tank runs dry (?). Zeros and mossies seem to be especially prone to catching fire and flying around shooting things for another 20 or 30 seconds before they blow up.
If the fire seems to appear randomly (aircraft not being fired at) and then disappears a few seconds later, I think that's a connection issue. I've seen it happen also.