WvW does not seem to give any Influence directly but since it’s full of events you would be getting influence from that. If you hover over each item in the History tab in your guild window it gives you a break down of where the influence came from.
WvW typically falls under PvE for all intense and purposes (they use the PvE skill breakdown). I’m pretty sure the PvP influence buff is only for any activity in Heart of the Mists (PVP land).
Whenever I’m on my bank guild, I earn influence in WvW from the events only, so I would imagine that anything that increases influence from events would affect it and not anything that affects sPvP
