In theory, at least, that setup should work just fine. I had a similar setup for years when I had my own router as well as Fios TV service and Fios STBs. At some point in there, I also use a CableCard in the TiVo DVR with a coax connection fed by the same MoCA adapter. (This was a loooooong time ago.)
I would suggest making sure the MoCA adapter you use is the same MoCA standard (e.g., MoCA 2.0, MoCA 2.0 bonded, MoCA 2.5) that your STBs are using.
