From what I have played with all user Spot colors are saved in a file called userinks.cpl. There does not seem to be a way for Corel to embed the color palette
into any type of output file.
For a test I create a Gerber Spot Foil palette (all colors saved in userinks.cpl), create a simple job with a number of these colors and saved the file. Renaming the userinks.cpl file and opening the file I just created yielded a number of things, one Corel not finding a userinks.cpl created one with Red, Green, Blue and Black colors and then "mapped" those colors to the colors I have in my simple job, Yuk.
Then I closed out CorelDraw, renamed the userinks.cpl file to it's proper name, reopened the file and all the colors and names were correct.
I have found and reported to Corel that created my own Spot colors and using a % of those colors and then exporting as a CMX file will yield a corrupt CMX file. I hope version 13 fixes this.
Networking, sharing the userinks.cpl file most likely will yield other problems since Corel seems to have this file setup in a certain folder and file read / writes by multiple versions of the app running could corrupt the file.