Does it make sense to use a portable amp such as Fiio E6 with a micro system or an A/V Receiver? will there be any benefit?
In simple, no. I don't see any benefit at all, unless you really can't get loud enough with it.
So the only upgrade would be a new set of headphones, right?
The most obvious upgrade is generally a set of headphone, but it depends on the whole rig as well.