My opinion is that if you're concerned about any chance of contamination, it would make the most sense to treat the water after you've thawed the ice and are ready to drink it. In other words, treat it close to the time of use, rather than up front. Even just adding some bleach should be fine.

It probably doesn't make that much difference either way, if you're careful about handling and storage, but in case something goes wrong that you're not aware of, it's logical that it's better to treat close to when you use it to be safest. Actually, I can't really think of any advantage to treat up front, unless you know for sure that the water source is of questionable quality, then I would consider it. As long as you treat at time of use, any accidental contamination of already clean water during the initial handling will be taken care of. I would consider pre-treatment up front if I knew the water quality was questionable because I will have the time and resources to properly treat it then and I might not have that luxury if I needed to heavily treat water during the emergency.

This reasoning may sound contradictory to what I said, but it's more a matter of risk management that dictates what to do. Like I said, if you're starting with clean water, the risk is very low even if you don't treat at all, but if you already know the water is questionable to start with, the risk is high. Say I wanted to hand out a frozen jug or two of questionable water to a neighbor to take home during some emergency. Maybe they said they have bleach but it turns out that they don't and can't boil that questionable water effectively, then they're definitely at risk from getting sick. Or maybe I grab a frozen jug before heading out for supplies or something during some emergency and I forget to bring a filter or tablets along. I sure would've wished that I had treated the water up front since I alredy knew the water was questionable. Would I risk drinking that jug on the road? I probably wouldn't.

Anyway, just my overthinking ramblings.