She is NOT a member of the elected government of our country, IF that still matters.
There are plenty of members of our government who are not elected. In fact the vast majority are not. The office of the First Lady has a USG staff and is part of the WH budget. Presidents have been using private interlocuters for as long as I can remember to deliver messages.
There's a host of other means to deliver "personal" messages.
It depends on the substance of the message and how confidential you want to make it.
Well, we haven't seen any reports from the MSM and probably won't be seeing any. So, if for example Michelle were conveying her husband's message that the USA would stay out of any conflicts that an Arab state might have with Israel, and any peripheral quid pro quo deal emanating from that information, that would be a very substantive message that would required lots of confidentiality.
Of course, since the MSM isn't and won't be reporting about plans for the meeting or the events of such a meeting, we are left to speculate.