Can the hard drive on which you store files affect your sound?
Sorry to disagree, but no, it can't.
The role of a NAS is to produce a string of ones and zeros, the only variable is the speed at which it does it. If it's suitably specified and is capable of keeping the buffer on the streamer filled, then there is no possible way it can influence the resulting sound.
You might as well ask if your choice of hard drive would affect the numbers in your spreadsheet, or the colours in your holiday photos.