All pvp gear states, "materia active during pvp only", so no, it'll never be active during PVE.

The thing is, in the df listings for all pvp duties it also states, "During PvP, materia bonuses are ignored"

What often happens is people assume that the statement on pvp gear overrides the duty finder statement, because it'd be pretty absurd for the game to tell us "materia in this gear doesnt work outside pvp, except materia doesnt work in pvp either". So you'll sometimes hear people say that "only materia socketed to pvp gear works in pvp" or "only pvp materia in pvp gear works in pvp", but neither of these is the case. PvP gear having materia sockets, and the wording surrounding them, is easily the most absurd thing in the game imo.