This is currently not possible on a per-user basis. You could have a custom script that reads the person's recorded name and then has a standard message that doesn't include leaving a message (e.g. 'Thanks for calling I am not in the office; please call back later. Good-bye'). The user could then forward their phone to this custom script when they want that feature; if they forward to the regular voicemail, then it'll take a message as expected.

Not the ideal solution, I realize, but maybe something to consider.