Yes, some of the newer glues used in plywoods can cause issues with a laser. Best to try some samples before buying a lot.
We have cut G10 fiberglass, it is not pretty, but it does it. Lots of charring. (We do have 150 watts to play with)
We have cut 1/2" plywood with pretty good results. We do not do it in a single pass, nor at high power.
We mostly but 1/4" birch ply or thinner woods, a bit of foam, fabric, acrylic, vinyl, cardboard, G10. I'm probably forgetting a few.
We can cut very thin metals, but only as an experiment. Don't bother!
Since we use ours for production, we use a lot of templates for alignment of materials. Sometimes this is plywood, but more often we use cardboard or masking tape for this.