This is not an established concept in English, so I can't give you an objective answer. However, I do think I understand what your colleague wants to tell you.
- Mutely = I am not going to ask you to bring chocolate
- Appreciated = ...but I would enjoy it if you did.
I think he's jokingly trying to avoid confirming that he wants them (so he doesn't seem overeager), but telling you that he would like them.
Another slightly different interpretation would be
- Mutely = I will never say out loud that I like them
- Appreciated = ...but I do like them.
Pretty much the same meaning, slight difference in interpretation. But the joke stays the same.
Edit In case you think it's a typo, these are the closest English equivalent phrases that I can think of:
- Much appreciated
- Hugely appreciated
- Duly appreciated
- Dutifully appreciated (very different spelling, but it sounds similar enough. Maybe he is repeating something he heard said and misinterpreted it)
The comments seem to think this is a typo, and he intended to say "mutually appreciated".
However, I don't think this makes sense in the context you provided. "Mutually" means for both parties, which in the context of a conversation is you and him. Why would he say that both you and him would appreciate it? You were asking him if he would like it.
It's not impossible that he meant "mutually appreciated" but used it wrongly. But if we can't trust the writer of the message to use correct words, then no one can be sure of anything anymore and the entire question becomes impossible to answer.