I agree there will always be Spartans, but not necessarily trained Spartans. It's not the Spartan blood that makes them Spartans, it's their culture. If you wipe out a generation, who will pass on their training? Also, if it comes to the crunch, everyone will be pressed into the army. Whenever a besieging army attacked a city, everyone, young and old would be called on to fight. After all, it was literally a last ditch attempt at life.

So yes, I think it is realistic that you can't train Spartans even if you conquer Sparta.