You should be OK installing Avaire under the vanity. The tiles under the vanity will be "locked" in place by the extra weight. The only thing you might watch is the grout lines where the "locked" tiles meet the "non-locked" tiles - I don't think you'll see any issues, watch for hairline grout cracks since that "interface" will not be a truly floating interface.
I have a very heavy desk and credenza on my Avaire floor (more than 2 years now) and there are zero issues!
Let us know how it turns out!
Thank you for considering Avaire!