If I delete a ts file from the DVR library, will that episode be rerecorded? Or is there a separate registry?
It depends on your settings… It doesn’t track individual entries. It will either record new and repeat airings, or new airings only.
If you have it set to new and repeat, and you delete your file… it is entirely possible that it could be picked up again.
So does that imply that, when set to include repeat airings, it will rerecord things already on disk and overlay what previously existed?
No. If the recording already exists it should not be recorded again, unless you have the replace lower resolution items selected and the new airing is a higher resolution than what is currently recorded.