We currently have an Exchange 2010 server on AWS. We want to migrate to Office 365, and have a free non-profit subscription. We are not ready to make the move yet to Office 365 but need a better backup solution (we currently only have AMI images on Amazon, which are costly, and are a temporary fix to a larger issue) then what was in-place from the old IT consulting firm. That being said is there anyway we can make a hybrid solution, where we simply use Office 365 as a backup for the On-Premise exchange server? We have setup a hybrid solution where users are on one or the other, but can they be technically "on both". Then when we are ready, all the data will already be there, and we can finish the migration quickly.
DISCLAIMER: While the below "should" work...I'd be cautious about undertaking it as your "backup" solution, as that's not what it is designed for.
Because you haven't setup O365 at all, in theory you could do the following, assuming you plan on going to O365 within 60 days (I believe that's the limit):
Note: this only handles mailboxes, not public folders or anything like that.
Basically what you'll be doing is a cutover migration but you'll be taking your time doing it. If all mailboxes sync within a few days, then at that point if your Exchange server on AWS fails, you could basically force the finalizing of the cutover quickly (MX records at this point, finish the cutover wizard, etc.) and retain all the email up to the last sync (happens every 24 hours or manually).
That's about the best I can think of.
No. You cannot make an O365 instance be a "clone" of your own Exchange instance. A single mailbox can only be in one or the other.
You can also not stretch a DAG between your Exchange server and O365.