Can a Dishwasher that automatically opens the door damage my kitchen cabinets?
If your countertop, especially the lip that overhangs the dishwasher, is constructed with particle board, you can expect damage. The particle board will suck up any and all moisture coming out of the dishwasher. I have heard that even granite tops can get discolored from the steam you're referring to.

You can coat the bottom of a particle board top with some exterior wood glue or silicone sealer to prevent the moisture from being absorbed. If it's granite, get a stone sealer and just apply to the bottom part of the lip.