From http://republicwireless.com/how:

  I have DSL at home.  Will it work on that or will I have to upgrade to
  something faster?

  You need about 80kbps both ways to hold a call. The more bandwidth the better
  for improved call quality. Don’t forget that streaming video or downloading
  large files all use bandwidth, so your mileage may vary if you are trying to
  make or receive calls and watch Netflix at the same time.

Sounds like it's more likely that your gaming or Netflix would adversely affect the phone than the other way around, though a router with QoS should fix that easily enough.