If it's covered, I don't see why not, but if you're using an open slat design, you're probably gonna want to have an open design in the bottom of the drawers too. Covers leak. I opted for just an open area under mine partly due to this and keep everything in storage bins instead. Figured that if it's going to be covered anyway, the unsightly aspect of the plastic bins is pretty much mitigated.
Here's a pic of mine:
It's ipe and white oak, so that in and of itself kind of makes it weatherproof, but the cover helps keep it from getting an aged look. It's been outside / under cover for 3 years now in Georgia weather and still has that same color, plus a bunch of grease stains on the top to go with it
One design feature I really like is that the grill is offset to one side vs being in the center. I really like having one large work area rather than two small work areas. I've never really bought into that workflow of having raw foods on one side and cooked on the other.