Of course that is possible. Just create a vSphere backup job. Guest file system indexing is not relevant in this case, so don’t activate that. When I backup Linux VMs, I don’t activate application aware processing, you can activate quiescence in the job itself. Don’t combine Windows VMs and Linux VMs in one job because it is recommended to use application aware processing for Windows. You could use exclusions in the job not to use application awareness backup, but is not possible for quiescence (is for the whole job). Therefore not combine Windows and Linux VMs in one job. Since other settings depends on other things which is not known, leave them default.

Check out this article by the ever awesome @vNote42 

VMware vCenter Appliance: image backup is deprecated since 7.0 | Veeam Community Resource Hub

In essence, yep possible, but it’s going away in the future so just be mindful of that.

https://www.veeam.com/kb2328

I tried using the VAMI interface but in 6.5 only FTP, FTPS, HTTP, and HTTPS are supported.  having issues making the connection to a Data Domain using any protocol

Backup the config to a webserver or FTP Server (VM on your Host). then you can backup your vm with Veeam to the datadomain.

For last but not least, try to do this backup not together with other VM’s.

I would recommend to update to at least VCSA 6.7 (U3). There you can schedule file-based backups in VAMI. Furthermore you can define how many restore-points should be kept.

… next to the advantage of not needing Flash any more.

Yes I remember when they first brought in those backups in 6.5 I believe.. I said great… now where is the automatic scheduler? oops there is none . That must have been a big feature request to say the least.

Yes, was some kind of version 1, without many features

I used VAMI to backup to a NAS via FTP then used FTP client to download the files to the DataDomain using the SMB2 connection mapped as a local drive.

If you really want to automate this then look in to PowerCLI and scheduling something in the Windows Scheduler to run.  You can set it up to run the PS script to back up to your NAS FTP and then look to automate the other parts as well maybe.

An example script for VCSA 6.5 - Backup vCenter Server Appliance (VCSA) 6.5 Using PowerShell – Virtualization, DBaaS & Whatever Crosses My Mind (magander.se)

Personally, I won’t use this method if I ever need to restore my VCSA. I will use Veeam to restore the whole image. I just think it’s easier personally. Though it’s not really an ‘officially supported’ method by VMware..it still works as it has in the past (if it was ever needing to be restore). 
Although, to VMware’s point in their restore method...their process is kinda similar to how Veeam suggests restoring VBR (build new server, then restore DB config).

Cheers.

I'm with @coolsport00 . The image based restores were very reliable until now, so I would always try them and use the official restore as a fallback.

We had an upgrade case lately which went sideways. We discovered the backup was falling and the engineer was unable to restart from the Veeam backup. The FTP helped to deploy a fresh version

As a side note, VMware allows only certain upgrade path even you are using the same branch (https://interopmatrix.vmware.com/#/Interoperability ). e.g. express patch on vCentre isn’t allowed/supported to upgrade to major. You can also have differences in the DB version, schema, and the FTP,FTPS, etc.. stays the easiest way to quickly identify it since it is part of the filename scheme.

Image restore isn’t reliable enough.

Oli