I think this only makes sense as an opt-in from the moderator that wishes to write the message. The thing is, this veil of anonymity is probably not going to work very well.
I've seen this in action with Impraise, where all of the feedback you receive is free-text, but you do not "know" who wrote what. In reality, it's usually pretty trivial to tell. There is science behind that: this talk claims that even with something as dry as source code, even when you ignore the variable names and only look at the structure of the code of the program you write, even when you make it obfuscated, a computer is able to attribute who wrote what between a pool of 20 authors or so with 80% accuracy in the worst case scenario.
In other words, unless you pick a template and don't touch it, you're not going to be "anonymous."
I would suggest that if you feel uncomfortable at all contacting a user — that's what other moderators and community managers are off. A veil of anonymity is probably only going to give you a sense of false security and the receiving user a burning urge to discover who wrote what rather than focus on the message that has been received.