If we are talking about a music server only with no on-board streamer, then teh connection between the external streamer and the server is a basic client/server data connection like any other application on a network. THere is absolutely nothing there that has to do with sound quality, just data transmission from a to b.
Now, say the connection is too slow, and the data cannot be provided to the streamer fast enough at full resolution. In this case it is possible that the streamer could negotiate with teh server to provide a lower resolution data stream that could easily impact sound quality upstream.
THis is all speculative but technically possible. The other possibility if the connection is poor is that the streamer has to wait for more data and pauses the music stream to the DAC accordingly until it receives all data needed.
SO two points:
1) the connection from server to client (streamer) makes no sound. The only issue is can the data be provided fast enough or not and that is more about the strength of teh connection, especially if say the connection is via wifi/wireless rather than wired ehternet.
2) The connection from streamer to DAC is where sound quality is more likely to suffer, assuming an adequate network connection is in play upstream as described above. Timing errors can occur between streamer and DAC (jitter) and greatly impact sound quality if not addressed. It is even possible with wired network connections that say one server introduces more noise into the network than another and that noise finds its way into the signal path from streamer to dac and adds jittter. The good new is many good quality modern DACS are jitter resistant and do reclocking themselves as needed.
So the devil is always in the details case by case even with the same gear in play. The details for digital streaming are much different than those for traditional analog gear alone. If swapping music servers alone (not streamer or DAC and same quality network connection and exact same source file at same resolution and same format)) makes a difference in sound, most likely it is introducing more noise into a wired network connection and teh streamer is allowing that to leak into the signal path to the DAC, and maybe even teh DAC is not jitter resistant.
Cheers!