Welcome Amy! We regularly work with 1/4" plywood (which is actually closer to 0.21" if I recall) and it cuts like butter. We haven’t tested 1/2" much but it should work with multi-pass (easier but rough edges) or double sided (have to flip it but cleaner edges) cutting; just expect it to be more than twice as slow as the cut time is more than double when the material is twice as thick.
The big caveat is - it depends a lot on the material. Some plywood is magnificent and some is terrible. It depends on obvious factors like visible quality (knots are bad) but also on invisible qualities like the chemical composition of the glue and the species of the interior plies. There’s no way to know if it’s cuttable without cutting, and no way to know if it emits harmful fumes without testing. So we recommend buying only plywood that’s intended for lasers, from companies like Inventables, Bur-Lane (like in this thread!), Laserbits, or us.