This is a high level mixer, it needs at least +10dBm to work at all, and then its performance will be poor. All diode double balanced mixers need enough power to be able to fully turn on the diodes. In a low level mixer this is two diode junctions in series, in these high level mixers it can be 4 or 6 junctions, sometimes with series resistance as well.
There may be thermal problems with using a high level mixer as a phase detector., it depends on the accuracy you need. I have in the past used +23dBm LO mixers in an IQ detector and that was quite problematic to compensate over a wide temperature range.