Yes, it can be done quite easily.
1. Grab a copy of /usr/share/ssl/private/domainname.key and /usr/share/ssl/certs/domainname.cert and /usr/share/ssh/certs/domainname.cabundle (save them locally somewhere)
2. setup the domain on the new server, etc, give it its own IP, etc
3. Go to the ssl/tls section of whm and click on "Install an SSL Certificate and Setup the Domain"
4. Paste the cert in
5. Then the key
6. Then doublecheck the domain, user, and IP (it may have automatically filled some of those - enter any it missed - if it doesnt supply a cabundle, paste the cabundle too)
7. Click "DO IT"