It's probably not a good idea to move thumbnails or even back them up. Just let MC rebuild them if necessary.
If you're having problems with thumbnails, use MC Tools/Options/Tree and View/Thumbnails and do:
Erase
Build Missing
For me copying the thumbnail folder is absolutely necessary. My MC12 thumbnails are currently 264 MB (The MC11 thumbnails take even more space). Creating them from the scratch takes almost two hours from a local HD. Creating them over LAN would take even longer. I maintain the library mostly on one of the PCs that has the files available locally and copy the same main library to the other PCs. I have configured the network so that all PCs can use the same directory paths for accessing the media files.
I need to update the database almost daily on the other PCs. As said earlier, a library restore needs to reset the thumbnails since they would otherwise be out of synch. The only working solution is to copy the library files and the thumbnails to identical locations to each PC (Naturally all MC instances must be closed during that.) If this is done correctly it is safe.
On the fly thumbnail creation is not an alternative for me. It would slow down everything, especially on the PCs that access the media files through the LAN.
The thumbnail path string in the Windows registry is just a standard folder path. The path can be any legal path that points to a local HD, but it is good to keep it short. (Mine is C:\MC12lib\tn\.) After it has been changed MC uses the new path exactly the same way as it used the default path. Also the default path varies from an installation to another because it contains the user name.