Invertor power source
In an idea world no, but in theory yes. You need to know the maximum current the inverter will draw, and then add this to the maximum current your amp will draw. Then ensure the wiring supplying the amp is able to carry this load. Additionally then the fuse already in place for the amp will need upgraded to blow beyond this expected total current.
The danger you run is that with only either the invertor or the amp running you'll in effect have a circuit with too heavy a fuse i.e. the fuse won't be so good at doing it's job.
And if you're an audio purist you really don't want to be attaching an inverter across your amp. Inverters can create some odd noise effects as the DC load fluctuates and electromagnetic interference is a factor with the inverters AC output.
So if it were me I'd run it to the engine bay.
I'm an electronic engineer with no knowledge of car electronics, just know the theory, so someone may come along to correct me....