You can go to P9860 and look in the far right column "Function Location" to determine whether a BSFN is client-only. Then you could search the compile logs on the enterprise server for a full build (or an update that includes your BSFN) for the presence of the desired BSFN.
For example, B1200001 is a client and server BSFN. Searching the C:\JDEdwardsOneWorld\ddp\B7334\packages\packagename\CompileLogs directory (and sub-directories) on your enterprise server for a file containing the text "B1200001" reveals a file named b1200001.log that indicates that b1200001.c was built.
Doing the same search for client-only BSFN's nets no results, indicating to me that the answer to your question is no- client-only BSFN's do not build on the server.
During the build process the source (.c) and include (.h) files are transferred to the enterprise server. I would imagine that the code for this step is where the client-only BSFN's are excluded.
