Yes, this is how I've transferred certificates before. But as you've said, the CSR is not necessary for the site to work properly via SSL / https. I only did it for completeness.
The certificate is stored in both the Plesk PSA database (certificates table) as well as the file system. If you'd like to transfer your certificate along with the CSR, do the following:
- create a new CSR for the domain using Plesk (you can use whatever information you'd like, we're going to...