No experience with Zerto itself but here are some thoughts: FMS is not Volume Snapshot Service aware, a lot of backup software use this underlying Windows VSS technology.
What this means is that if the backup software pulls a snapshot, the FM files that are on the snapshot will be in the 'improperly closed' state as a minimum, and will say so when you try to open them. Worst case FM will report them damaged when you open them.
The reason is that FMS was not able to put the files in the proper state and flag them as safe to be copied.
So don't rely on anything like that for a backup strategy for the FM files itself. It may still be useful for a backup strategy around the FMS installation and machine state itself, but not for the FM data.
You can use the FMS fmsadmin CLI to put the files in the correct state for a snapshot by issuing an 'fmsadmin pause' and an 'fmsadmin resume' when the snapshot is done, but trying to get the timing right with the backup schedules for the other software often proves to be extremely tricky and that will make the backup strategy fragile and unreliable.
If the other software can issue the CLI commands just before taking a snaphsot then it would work.
Thanks for the answer. Will be meeting with my IT guy later and will report back for others who may be in the same boat.