Here is what I did.
Created new backup job. Ran the job to the C:\veeamrepo folder
I then created a share on another PC and shared it out to a domain user called veeam.
I changed the options and changed the destination to \\OtherPC\Sharename
I had trouble so I changed the Veeam services to logon with the veeam user account.
I still had trouble connecting and received this error when trying to run the veeam for O365 backup:
10/12/2016 6:32:20 PM :: Connecting to remote server failed with the following error message : [ClientAccessServer=XXXXXX,BackEndServer=XXXXXXXX.namprd04.prod.outlook.com,RequestId=XXXXXX,TimeStamp=10/12/2016 6:32:20 PM] Access Denied For more information, see the about_Remote_Troubleshooting Help topic.
I then changed the repo destination back to the C:\veeamrepo folder. I know get the same error.
I try to create a new backup job, and it can't connect to the mailboxes with the org domain credentials.