Short answer: No.
If you come to think of it, you might be pleased to have people consult you on problems, but not so pleased to have other people ask you to read stuff. MathOverflow has enough curious people on it who like to choose what they read without hints from others they may have just met.
Long answer: There are ways. Primarily though, it is about building a relationship. If you establish a history of being interested in a person's work (and well-being, including giving them personal space), then you might ask if that person would look at something of yours or of someone else's. However, the primary function of MathOverflow is to build a database for use by the community, not just for a set cadre of experts.
So use MathOverflow to craft relationships as well as make yourself attractive (in an intellectual sense) by posting your material and crafting it so that it is beneficial for the non-expert as well as the expert. The expert might come to you wanting to know your thoughts!
Gerhard "Sometimes Loved For My Phrases" Paseman, 2015.09.06