If the warrant is valid, I don’t see how anyone affected by the raid has a case. If the police serve a warrant on the house next door to you, and your street gets blocked off while they go over the building with a fine-toothed comb and carry off evidence, it will be damn inconvenient for you, but I don’t know of any law preventing them from doing it.
Oh yeah, and they're searching through your store as they make their way to the location on the warrant.
In the case of a shared server, I don’t see how you can do a good forensic search of the affected server without having the physical box in your possession.
One wonders whether their actual goal is not to gather evidence, but to actually interrupt the service.