Sure, but there's a simpler and already-well-accepted convention for doing this. Say "interpreter" if it takes a program and causes its effects to happen, or "compiler" if it takes a program and emits an equivalent program. If somebody says "transpiler", just mentally replace it with "compiler". Done!

Composition of compilers still works as normal. You can use tombstone diagrams to reason about complex chains of compilers and interpreters. And it demystifies the act of building compilers, which is important because otherwise you'll be shaming junior engineers for attempting what is not just the pinnacle of computer science but also our bread and butter.

Seriously! Of all the definitions of "transpiler" that I've heard of so far, "compiler but shitty" is the worst yet.