In practice I don't think it's an issue: Metformin has been used to improve body composition at least since Dan Duchaine recommended it back in the 90's, and has worked fine.
On the science, a couple of things suggest improving muscle protein synthesis, at least where there's a burn injury:
Now, the burn state could be different.
I don't know of any scientific evidence showing reduced muscle protein synthesis with metformin.
Personally I wouldn't worry about it: it works well in practice.