It's unclear, but in narrow AI we've seen software get smarter even in cases where the hardware is kept constant, or even made worse. For example, the top chess engine of 2014 beats a top engine from 2006, even when you give the 2014 engine 2% the computing power of the 2006 engine. That would seem to suggest that an intelligence explosion without hardware improvements might be possible, at least in principle.

In practice I would expect an intelligence explosion to lead to hardware improvements as well, though. No reason for the AI to constrain itself just to the software side.