Yes, but if in searching my neighbor's property they were poking in my living room that would be an illegal search of my property. I'm not sure which metaphor is stronger, but it's certainly not a clear case either wya.
If the warrant includes your living room (because the police have probable cause to believe that there is physical evidence in your living room that would link your neighbor to the crime), then they can search your living room.
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.
If the system in question has RAID disks, it should be sufficient to grab one drive (depending on the RAID configuration) from the array. The FBI could take that home and examine it, while everything actually running on the server remains uninterrupted.
One wonders whether their actual goal is not to gather evidence, but to actually interrupt the service.