Do snapshots retain the IP address of the Droplet they were created from?

No, snapshots don’t retain the IP address of the Droplet they were created from.

We assign Droplet IP addresses automatically and they cannot be manually reassigned after creation, but you can assign a floating IP address to a Droplet and then reassign the floating IP address to other Droplet’s as needed. This allows you to maintain the same IP address in your infrastructure but gives you the flexibility to point it at different or redeployed Droplets.