That's exactly right.
The Recovery Services Agent running on your Hyper-V hosts will replicate (block level) the disk changes up to the Recovery Service Vault (down to every 30 seconds for critical systems if needed), so if you have a disaster (either your entire on-premises datacentre goes up in flames, or even if one of your servers starts to blue screen), you can failover the servers up in Azure and continue to run the server(s) up there while you fix your datacentre.
When you initiate a fail over, the platform will copy the data out of the Vault, create the VM disks from it, then create the VMs associated and spin them up.
The few things to be aware of:
- Make sure you have the network design done and setup well before a disaster. This involve creating the virtual networks in Azure (to which your VMs will connect to), as well as the connectivity to the network (and therefor your servers) should your datacentre becomes inaccessible.
- Beware that the bandwidth required from your datacentre to Azure has to be sufficient to sustain the rate of change and upload of the data to the vault. This is also valid for the disk access once the VM is in Azure itself.
Microsoft has developed an assessment tool that will calculate it all based on your existing workloads: found here
- I would recommend to have your network in Azure connected back to your on-premises network and to deploy a domain controller up in Azure. That way, you have an existing domain controller always available should your datacentre go down (Domain controllers are a bit hard to failover due to the IP addressing change as well as the domain topology, so it's easier to have one already up and running as opposed to failover your existing ones).
I did a quick Azure Site Recovery demo video, and although it's a bit old now (about 3 years ago) and the tooling/portal might have slightly changed, the principles in there are still valid, so worth watching:
Feel free to reach out if you have more questions :-)
(and don't forget to mark the answers as accepted if you feel I've answered the questions correctly :-))