The answer, unfortunately, is no. While a trustee may lawfully possess assets of the trust, when he/she goes to the dealer to pick up the NFA firearm, after receiving approval from the BATFE, the trustee must fill out a 4473 and a NICS check. For a 4473, the individual must be a resident of Pennsylvania. Thus, the trustee must have some form of identification showing that he is a resident of PA in order to pick up the NFA firearm from the dealer.
That being said, this does not prohibit an out of state trustee from possessing an NFA firearm that is already in the possession of the trust. Hence, if you are a trustee of a trust that was enacted and is situated in a different state, you may use the NFA items in that state where the trust is situated. If you desire to possess the NFA firearm out of that state, you must file a temporary or permanent move of the firearm with the BATFE, using Form 5320.20.