In principle, this should work - I haven't tried it, but in Conversations, the fingerprints of my other connected devices show up and I can say that they belong to me.

In any case, there are no desktop clients yet that support OMEMO. Conversations and Jitsi support Message Carbons though (together with a compatible XMPP service, such as yax.im) very well. On the console, there is profanity that also supports it.