I can see a few flaws in your reasoning, viz:
1. The float valve, in your scenario, wouldn't open until the system cools, so any fresh water in the cistern won't be drawn into the system until the cooling cycle after one in which it was admitted to the cistern.
2. Given point 1 above, I expect that any fresh water drawn into the cistern will contain no more oxygen (whether free or otherwise) than water that had been sitting in the cistern a long time (e.g. months).
3. Notwithstanding point 2 above, if any more-than-averagely-oxygenated water did enter the system, it wouldn't immediately appear as bubbles in a radiator - it would be rather more likely to accelerate the corrosion in the radiators, releasing Hydrogen as one of the usual suspects in source of the corrosive reaction. If this has happened, then the action you need to take is the same as if the system were sludged up.