I asked, because Bluetooth shares the 2.4 GHz range with WiFi and pairing a Wii Remote with Remote Buddy can increase traffic over it, leading to more collisions. In that case, connecting to WiFi over a 5 GHz range is the solution.

If you're accessing your Drobo via Ethernet, I can't see how the use of Remote Buddy could directly affect your network performance. It contains no code that could.

I can, however, imagine a possible indirect effect of one option:

At Prefs > Movie Library, Remote Buddy offers the option to automatically find VIDEO_TS folders using Spotlight (on by default). If the index Spotlight has built isn't sufficient for Spotlight to serve the results to Remote Buddy's query, Spotlight might perform a full scan of your network drive - which can result in a performance hit when you access that network drive at the same time. You can turn off this Spotlight search at Prefs > Movie Library.

Best regards, 
Felix Schwarz