The water heaters without an anode rod are made by Atwood. They have an aluminum tank which serves as its own anode. So, essentially, they have an anode, it's the whole tank. In that brand, RV antifreeze will cause corrosion/pitting of the entire tank surface (where the antifreeze is in contact with the tank. So to answer your question, yes, it matters that you keep antifreeze out of the Atwood water heaters as well as out of the Suburban water heaters (which are made with steel tanks, coated with a porcelain (glass) liner).
If you do get a bit of antifreeze in either type water heater, it's not a crisis, just flush it and keep on going. It's the prolonged (all winter) contact that causes damage. It also probably won't cause enough damage to render the tank useless the first year, maybe not the second year, but eventually, the accumulated corrosion over time will render the tank useless. That time may be 5 or 6 years for one with antifreeze in it versus 10-15 years for one that's not exposed to antifreeze. So, it makes a difference, but not something to call an "emergency situation".....
2015 F250 6.7l 4x4
2014 Cougar X Lite 27RKS