Thats a good idea. If I know the person I am challenging I would usually send them a short message anyway after sending the challenge. It would nice to be able to send a message with the challenge.
Leaving a message with a game challenge
In my opinion, if he/she challenges it means he is willing, why he/she challenges is not our look out, if we wish to play u hve to play , thats all brother u enjoy the game rather than thinking more because chess exhaust u r brain fully.then why additinal load to u r brain. dont thing otherwise any way i welcome u r idea.

That's be nice. Sometimes I recieve a friend request coupled with a challenge from somebody I never saw play, post, or anywhere else. I mean, why don't they just create an open seek with a rating range to play somebody of a certain rating?
Isn't it nicer to receive a game challenge with a message from the challenger telling you why he/she wants to have a game with you? Unfortunately, on chess.com, there is no provision right now for the challenger to be able to leave a message with the game. I think if you know the challenger's intentions, it is easier to decide whether to accept or reject a challenge. Moreover, you will have something meaningful to say when you choose to reject the game. What do you think?