When publishing a map service from ArcMap these warning are expected as ArcGIS sees them as custom. However, they should be warnings not errors. In essence they should not prevent you from publishing the service.
Yes, installing the Object Reader on the Server allows for the ArcFM Objects to be read from the service. However, as you indicated, there is not something to say that the Object Reader is there from the client. You could try to publish a test service and consume it in a viewer where you can select a feature and inspect its attributes to see if it is working correctly.
In short, there is currently not a way to show from the publishing client that the Object Reader is installed; but the warnings are expected.
Let me know if you have any questions.
Yes, I can publish with the warnings. However, when I do, only the non-network features were present in the map service. I'll confirm this, in the morning, and let you know if it is still a problem (I switched to the Minerville .gdb).
Moorhead Public Service
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There are two versions of the Object Reader: the 32-bit one meant for ArcGIS Desktop products and the 64-bit one meant for ArcServer. Do you know which one got installed?