I have 3 MXS 2013 in a DAG.

Server 1 - has 10 active databases - passive copies to Server 2

Server 2 - has 10 active databases - passive copies to Server 1

Server 3 - has all 20 passive databases from both server 1 and 2

I have Server 3  backed up to an offsite location.

If all 3 servers completely fail and I only have a full backup of server 3. Will restoring Server 3 and activating databases on it, bring me back online??

No it will not because the DAG will not have enough members for a Quorum.  Exchange 2013 has a 'Dynamic' DAG where if you shut down nodes in sequential order, the DAG will update which nodes are up and down and a cluster can operated on one node in this fashion.  In a DR scenario where all servers get shut down, when you try to bring them up the DAG will want Quorum and cannot achieve with one node.

For Server 3 to come back online, you will need to remove the other members from the DAG, leaving you with a single node DAG (this is the simplistic view) and then you will be able to bring them up.

Hope this helps

Thanks,

Jason

Temporarily remove the other members from the DAG and activate the databases on the single node DAG. I can then rebuild the other servers and re-join the DAG later correct?

With a temporary single node DAG scenario. I should be up and running within a few of hours :)