That sounds reasonable, but unless everything we saw about Quirrel is lie, he is unable to cast animal Patronus, being cynical sociopathic rationalist with a homicidal tendencies.

There is some possibility that Quirrel have analyzed his conversation with Harry, words about "rejection of Death as a part of natural order" and picture of stars being able to keep Dementation away and re-discovered True Patronus (there is speculation about Quirrel being enemy of Death, so it at least plausible), but True Patronus couldn't look like a snake.

PS: Your argument partly applies to the Patronus of Lucius being a snake, though.