Eventually we are planning on moving our current site from MySql to PostgreSql and I'm also wondering the same question, but also interms of PostrgreSql, Mono and Dapper on linux?
I'm using Dapper with the official MySqlConnector on an OpenSuse machine (+ mono) and it works great.
Why not pull down the source and build it? Based on this comment from the Dapper home page:
Will dapper work with my db provider?
Dapper has no DB specific implementation details, it works across all .net ado providers including sqlite, sqlce, firebird, oracle, MySQL and SQL Server
...and Mono's ADO.NET implementation, I would think your chances are pretty good that the code will work with little or no modification.