Absolutely not. If you had a conventional mini fridge, that would be fine, but since we’re talking about thermoelectric coolers, you would ruin them. There’s something that’s called a peltier plate inside your unit that uses the thermoelectric power to cool everything down. When that gets wet, it can get damaged. If some condensation from the food you kept inside gets on the plate, wipe it off, but know that a few droplets aren’t going to destroy the whole thing.
If the ice is in a bag, if the ice is only going to be in there for a short while, it’s still not okay to store in your thermoelectric cooler. If you don’t have quality containers for items like soup, you also shouldn’t transport those. Keep liquid off the peltier plate, and you’ll be okay. We’d like to point out that if you look at many warranties on this product, they cover peltier plate (which may be referred to simply as a cooling plate) that fall into the category of manufacturer defect. If they can detect incompetence as the reason why the plate broke in the first place, the warranty might not cover you.