Is it possible to backup a LVM disk to an external server?

Yes.

Tthis is used widely, and it actually involves snapshots to ensure consistency of the backup.

For example, this is the way virtual machine (and container) storages are backed up in the Proxmox VE:

• Suspend the VM. There is no way to atomically make several snapshots in Linux, so the only way to back up all disks at the very same moment of time is to make sure VM can't do anything until all snapshots are ready
• Snapshot all disks. This process is relatively fast
• Unsuspend the VM. The time while VM was unavailable is small, up to the point it is not noticeable
• Send images of all snapshots to the backup storage. This is the long process. But the fact these are snapshots enables us to have consistent backup, while VM could still run. The state of the backup will be the moment when VM was first suspended
• Remove all snapshots.

This was the simplified description; actually PVE uses also some tricks in the Qemu to emulate snapshots on the backing storage where there is no such feature, but this is not relevant to the question.

Pros are already described. Cons I can think of are the need to have some spare space in the VG to store these snapshots, and the amount of the space is not possible to predict in general, it depends on the amount of I/O the VM is doing while data is sent to the storage, which in turn depends on the I/O rate, virtual disk size and network capacity. In practice, I never had any problems with this.

I described the particular use case, but whatever you backup, the details of the process will be the same.