Interesting question Absinthe. Thanks for asking, as it has made me confirm the functionality I describe below. I always knew it was there, and should work, but haven't had lots of success until now.
But first, I would have expected MC to already have a mapping from CATALOGNUMBER to [Catalog #], but it seems it does not. I don't know what populates [Catalog #], if anything. That is hidden in code. Maybe JRiver could look at it, and if there isn't any conflict, add the mapping. It may be that there is a mapping already there for movies or something, so audio doesn't have the mapping.
While I don't know of any way for a user to map from an external tag to an existing MC field, you can get the data into MC easily. Just create a new field in MC called CATALOGNUMBER making sure that the name including case matches exactly. You can change the Display Name for the field, but must use the exact same name as the existing tag for the new field. Then just run the "Update Library (from tags)" function for the files you want to update. MC will import the data.
EDIT: Just to be clear, we are talking about the "TXXX (CATALOGNUMBER)" tag in the files.
I created such a field, gave it a Display Name of "Catalogue #" and ran the update for a file I have used MusicBrainz on. The data appeared in my Library no problem. Then in a View where I had both [Catalog #] and [Catalogue #] displayed, I edited [Catalog #] and put "=[CATALOGNUMBER]" into the field, which copied the value from [Catalogue #] to [Catalog #]. I also tested the right-click "Library Tools > Move / Copy Fields" function to do the same thing, which worked fine. This is a multistep process, but it does get the tag values into the existing MC field correctly. It would be best if the values did get into the existing field name, for consistency with other media, but you could also just use the new field directly.
I really think JRiver should look at the mapping though, and add it, unless there are good reasons not to.
PS: I also looked at files I had ripped from CD and hence looked up on YADB, at the Album level. They didn't have any values in [Catalog #] either, which is a bit strange. I would have expected that to be a key piece of data in matching CDs to the YADB records.