If (theoretically) the great Temple was built again, would there be Kohanim pure enough (physically, etc.) to perform the worship and sacrifices?
The Raavad to Hilchos Nezirus 5(15) states that
הכהנים בזמן הזה טמאי מת הן
Kohanim in our time are impure with טומאת מת.
So, no there would not be Kohanim pure enough (physically, etc.) to ideally perform the worship and all the sacrifices.
But when all or most of the community are impure from contact with the dead, sacrifices with a fixed time are permitted טומאה הותרה בציבור, so in effect they would be pure enough for a great portion of the Temple service.