Is newly produced sperm healthy if there was previous DNA damage?
Male gametes (aka sperm) is produced by meiosis of numerous germ cells (gametes precursors). It is unlikely that all germ cells have damaged DNA so the newly produced gametes should be healthy. This also implies that if the DNA inside the gametes was damaged after they were produced, then again, the new gametes will be healthy.

As a disclaimer, I am talking exclusively about damages to the DNA, it could very well be that gametes are unviable for other reasons than just spurious DNA (e.g. low mobility). In this case, viable gametes are unlikely to be produced unless the reason underlying the original production of unviable gametes is fixed (e.g. via medication).