This wouldn't make a difference since all Teruma is d'rabanan even during the time of the second Temple according to the Rambam and still they were careful not to derive benefit from Terumah Temeah if they were not Kohanim, since the Teruma still belongs to Kohanim.

Rambam writes in Hilchos Terumos that Kohanim have the right to benefit when Terumah Teme'ah is burnt and Aba Shaul is seemingly stealing from the Kohanim. However the Rishonim state that he was doing this for the Kohanim in the house of Rebbi and this is why it is permitted (Tosfos)

Yoel Domb