Suppes gives a natural deduction system in his book Introduction to Logic (Van Nostrand Reinhold Company 1957). First he gives some rules for making sentential inferences, and then later for inferences involving quantifiers. One of the rules for sentential inferences is "Rule T" on page 28 which says:
We may introduce a sentence S in a derivation if there are preceding sentences in the derivation such that their conjunction tautologically implies S.
Then later, when he is introducing the rules for inference with quantifiers (example 1, page 59, reproduced below), he gives a derivation where he uses rule T on a nonsentence (he uses rule T on a formula with free variables). So apparently S does not have to be a sentence in the wording of rule T?