Honestly, the best way to handle remote paging is buy a Mitel 5212/5312 phone, get it registered on the controller remotely, open the phone, cut the speaker leads off and splice them to a cable coming out of the phone, and connect it to the 600 ohm/Aux/Phone page input of the amp.
The method you describe should work if setup correctly, although I think it would be less than reliable. The best way to test it is put a butt-set in to test it, I will almost guarantee that the system is sending the paging audio out, you can test that with any other audio source at the system end, a radio, tone generator, etc would suffice. My guess is that the back to back SIP devices are not "trunking" properly (Mitel would be the STATION or FXS side, Bogen would be the TRUNK or FXO side) because essentially you want the Mitel to go off-hook like a phone and it expects battery/dialtone from whatever it is hooked to. Another test would be to plug an analog phone into the MVP at the Mitel end and go off-hook, can you get battery/tone from the Bogen and page? If not, then the connection is not correct.