"... one battle die, in total, per battle phase" is a really weird phrasing. It must mean per battle phase per affected region.
This FFG answer clarifies the meaning http://www.boardgamegeek.com/thread/621300/greenskins-invade..., but in the clarification, the employee describes the effect as
In each region containing an Event token, each player who rolls battle dice may only roll a maximum of one battle die, in total. and in that meaning, it would absolutely affect rampage.