It’s not “highly likely”, it is guaranteed. It’s impossible to run an Exchange server without regular backups. The server would very quickly cease functioning.
The real question is: do those backup still exist or were they destroyed as well?
Gotta give time for the cleaners to do their work!
Circular logging and the exchange server can run without backups.
Are we even sure it was an Exchange server? And yes you can run it without making backups. But you are asking for trouble if you don't.