Yes, it would seem so. You could even simplify the rule in your own head by saying that the
only verb that may appear before あいだ is いる.
A Dictionary of Basic Japanese Grammar mentions "The verb before
aida is normally nonpast V
te iru or
iru, regardless of the tense of the main clause," but it doesn't list what the exceptions to this general rule might be. One exception shown in its example sentences, however, is "秋子は子供がいない間に本を読む。"
By the way, be careful about your 間s and 間にs. 間 means that the second event in the sentence occurred during the whole time of the first event. 間に means that the second event occurred during only part of the time of the first event.
Examples:
私は日本にいる間にキャンプをしました。
I went camping while I was in Japan (i.e., I wasn't camping the entire time I was in Japan.)
彼女がディナーを作っている間私はゲームをしていまし た。
While my girlfriend made dinner, I played video games (the whole time).
As a final note, with 間 or 間に, the subjects of the main and subordinate clauses can be the same or different, as illustrated in the two examples above (the subordinate, i.e. less important clause comes first; the main clause comes last). When the subjects are different, the subject in the subordinate clause is marked with が, not は. For the similar grammar construction -ながら, however, the subject of the subordinate and main clauses must be the same. -ながら also implies that the action after -ながら is more important than the action that appears before －ながら.
This page details some of the information I mentioned.