ShipWorks can run "in the cloud" as long as you are using a cloud system that supports running Microsoft SQL Server 2008 R2 (or newer) with CLR Assemblies and allows remote connections to that server. Once the database is running "in the cloud", client machines can connect to that database and share information.
Some customers have had success running ShipWorks on a hosted cloud server (like Amazon) or a virtual Windows environment (like Rackspace).
Note that even if not using a cloud configuration for ShipWorks, multiple ShipWorks computers/users can always connect to the same ShipWorks system while all computers are on the same LAN (local area network) or VPN (virtual private network). Please click here for more details about setting up ShipWorks on multiple computers for multiple users in a shared environment.