My family is subscribed to Office365, largely to get OneDrive. I am going to wait a few days for more reviews to come in and then probably try it on my iPad and droid phone.
I have a custom domain name for email and I use gmail. I would think that mapping a custom domain to Office365's email hosting and using gmail separately in the new apps would be well supported.
As others have noted, this is a rebranded Accompli. Reviews on Accompli should be relevant.
I find Accompli to be decent and I'm happy to see Microsoft move quickly with it post acquisition. I have noticed a few crashes on my Nexus 5, but in general it works well. I would recommend it over the Google provided Android solution.
I have a custom domain name for email and I use gmail. I would think that mapping a custom domain to Office365's email hosting and using gmail separately in the new apps would be well supported.