I found this page on the msdn which suggests that version 3.5 and above of MS SQL Server Compact should be o.k. in this scenario.
To support multiple applications that
access the same database at the same
time, SQL Server Compact 3.5 provides
multiuser support. Multiuser support
enables multiple users of a database
to synchronize data without having to
disconnect the database before they
use merge replication or remote data
access (RDA). For more information
about multiuser synchronization, see
Multiuser Access and RDA and Multiuser
Access and Synchronization.
However I, personally, have no experience with this so could not say for sure if this will definitely work.