If you've installed the 64-bit Object Reader, your work there is done. All it does is give ArcServer the .dlls it needs to be able to read and decipher the ArcFM data. The object reader only gives you read-only capabilities though.
To edit, you'll need ArcFM Server, which is an entirely separate product that has to be purchased.
Now the issue with you not being able to register the geodatabase has nothing to do with ArcFM. That sounds like a Oracle client issue (I saw another of your posts where you mentioned the clients). You need to have the 64-bit Oracle client installed. ArcServer doesn't care about what data is in the database when trying to register the connection, only that it can connect and communicate to said database.
I would not be able to sync without the ArcFM server , correct?