No, you should not make this substitution. Aaron's answer illustrates how these three most common Eb band instruments have different ranges. So some notes may already be impossible.
My answer is more from the perspective of the composer's intent. Chance wrote for a specific timbre, and just as you wouldn't want to just go changing some of his notes arbitrarily, you shouldn't mess around with changing a bunch of timbres either. The alto is a much stronger timbre and it doesn't blend as well as the clarinets.
Assuming you are conducting this piece, you'll have to weigh the importance of Chance's masterful orchestration against the need to balance your ensemble. If it means that a young person might get to play in this wonderful piece ONLY if you make this substitution, does that outweigh the desires of the composer? Maybe it does, maybe it doesn't.