I've discovered the answer to this question by unfortunate experience, so I'm sharing it...
I have an XT200 Weedeater Trimmer. In between the carburetor and the air filter is a thin metal plate called the Plate-Filter Support. Unfortunately, in the process of repairing it, I misplaced this plate, and could no longer find it. Is it ok to run the trimmer without this plate in place? It doesn't appear all that critical.
Pictures of the part:
The plate in place: