I'd really like to know the answer to this question also. I tried to use CMC gum as a transparent/inert binding for two sheets of film but I found that it was too strong and didn't dissolve very well, which was a problem because it was meant to be a temporary adhesive.
For instance, if you let a drop dry on your counter, it dries very hard and is difficult to get off. This would suggest that it might be an excellent substrate/sizing though.
Why don't you coat some different concenctrations on a piece of tissue paper, let it dry and see if it dissolves as is? I suspect that even this might be difficult.
Last thing I'll say is that I know of one patent wherein a very dilute solution of CMC gum is coated over a gelatin layer to produce an overcoat that inhibits the migration of mordants from the gelatin layer. This is for a dye-imbibition paper. So, it must be pervious to the dyes, but not this particular mordant.
It's an interesting substance, I'd like to know more about it.