Could treated water backflow into my RO system?
It can backflow if you lose pressure. Perhaps from a power outage, or if you draw water faster than the pump can replenish it.

Backflow valves (check valves) are pretty cheap (about $5 - $10). If the consequences are as severe as you make them out to be, I'd put one in.

Also I would add a carbon filter after the RO system, that would remove ammonia and other things, just in case. If the water was clean the filter would not get worn, so it's cheap insurance that you can leave there for a long time without replacing the filter.

PS. It's good you are not trying to drink softened water - the extra salt is not good for you.