Of course this is fine! New and old are welcome to volunteer, and this sounds like a good plan.

And yes, I was thinking something like that. Since of course we can't just clear through all the heart shards in a week, each heart shard encounter will be spaced out over the course of probably the next few months. The heart shards could potentially arrive in Luceti separately, so it can be up to the individual volunteers when they get infected/how long it takes for it to overtake the person/how long until Duck becomes aware of the shard.