If you power the NAS off completely, do the network issues disappear? Wi-fi can be effected by all sorts of things and it sounds like you're currently just going off of a gut feeling.
Honestly, my first step would be to get as much as possible on wired connections. This could be as simple as wireless spectrum congestion due to a neighbor getting a new wireless AP.
Then I'd be checking network logs for the synology. I would expect it to have some way to do that.
Beyond that, "network issues" doesn't give a lot to work with. Is it complete loss of connection, slow speed? And can you quantify it with any network logs or diagnostics?
If it was just from adding one more piece of hardware to your network that is sitting idle, I would expect you to have seen it before now with say, an extra cell phone on your wifi.