IIRC C2H generates large blocks of logic that can be used anywhere - but for nios access would most likely be accessed through an avalon slave, rather than through a custom instruction.
Whether you will do anything faster than your desktop rather depends on what you are thinking of.
Things which are difficult in software, but simple in hardware may be faster, as can be things like integer FFT - where you can throw logic and multipliers at the problem to get parallelism.
The other reason for using a nios cpu is to get guaranteed low latency - but in that case you probably wouldn't want to run any OS at all.