Do fuses affect a PC PSU's amperage output?
The answer is only very slightly as Ambiorix and PeterJ explains.

The thing to note with fuses is they are thermal devices and take time.

I have put 20A through a Fluke meter for more than a minute before it blew the 10A protection fuse. (I didn't know the fuse was 10A at the time or that the meter wasn't calibrated for it either ..oops )

There are different fuses but what you find is that a 10A fuse has to last (almost) indefinitely at 10A. 

The fuse blowing is an exponential behaviour. when you get to 2 times the rated current some fuses last 1 minute or more, at 2.1 time they may last 30 seconds and at 10 times they all react very fast... but it depends on the type of fuse.