Yes, there are drawbacks to buying a network laser printer instead of one printer for each PC. If your one and-only breaks down, printing for the entire office will come to a screeching halt. To prepare for such a scenario, level out the load with an inexpensive inkjet or a low-end laser. (Either one will get you through until the original printer is fixed.)
Another disadvantage is having to line up printing jobs, but you can overcome this by matching the print speed and duty cycle of one or more network printers to your office workload. Also consider space: Unlike the small footprints of desktop printers, network laser printers have large and bulky paper cassettes--sometimes on both sides of the printer--that require lots of elbow room.