I've been using an iPad mini 3 with my P3P and am thinking about buying an OSMO. Since I only carry a cell phone when I leave town a few times a year, I've been using an ancient cheap prepaid Tracfone. When I called DJI sales on 30 Nov., I was told that the only phones and tablets that would work with the OSMO were those listed on the website.
I decided to upgrade with a new phone from Tracfone, since I had about 3200 minutes built up over time, so for $89.99 I bought an LG L21G Destiny with Android 5.0, and popped in a 32Gb microSD card. Today I installed the DJI Go app, and did a test flight with the P3P, and it worked. So I'd guess it would probably work with the OSMO as well.
For anyone not chained to a cell phone, this would be an inexpensive alternative to paying $100 a month. For $90 for the phone and $100 for a year with 1200 minutes, in less than a year I'd have an OSMO with extras paid for, and the following years would be only $100 each.