The fuse provides a clue as to what the real power is. According to the manual, 10 amps max. That means they're lying about the 300 watts. The specs in the manual don't give any RMS power rating. So, I wouldn't touch it unless I was desperate and it was virtually free.
There should be worthwhile amps if you go a step up in quality. I had no problems with an Audiovox 4-channel amp I bought from Costco in the mid-90s. It provided RMS power ratings, was fused at 40 amps, and claimed to have thermal and output fault protection, all of which suggested it wasn't complete junk.
Good car audio has been around long enough that you can find good used amps for cheap. I picked up a made-in-USA 4-channel amp for $44 at a pawn shop. The outside could use some fresh paint, but the innards were pristine and functional. Try yard sales; people probably won't rip you off, because you know where they live. Antique car part swap meets usually have some car audio gear; occasionally there's a dude from a wrecking yard with a vast collection of stuff salvaged from crushed cars.