If a Poison-type Pokémon that is not also a Flying-type or have the Ability Levitate is switched in, it will absorb Toxic Spikes and the effect of Toxic Spikes will end.
Source: Bulbapedia/ Toxic Spikes
So since Crobat is Flying-type, the T-Spikes stay. Same rule if you sent, say, Gengar. Since it has Levitate, The T-Spikes are unaffected.