If you damage an invader and then replace it with another invader, will the new invader enter the game damaged?

If you damage an invader and then replace it with another invader, will the new invader enter the game damaged?

Yes. (Rulebook p. 18) When you replace a piece with another piece, the new piece comes in with whatever damage the original piece had.
For example, if you deal 2 damage to a city and then replace it with a town, that town will be destroyed immediately.
If you replace a damaged piece with two or more pieces (as when Dissolve the Bonds of Kinship replaces a City with two Explorers), the damage (and Strife tokens, if applicable) get divided between the new pieces as you choose.