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 reserved IP address to a Droplet and then reassign the reserved 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.

Reserved IPs do not support SMTP traffic.
You cannot retain a Droplet’s IPv4 when you transfer the Droplet to a new region. Use a reserved IP address to maintain a static IP address.
Take a snapshot of your Droplet and then create new Droplet from the snapsnot in the new datacenter.