Jamal,
If you refer to a "published mxd" meaning an ArcGIS Server map service (a service you create by publishing a map document in ArcMap), then you are correct. It will take more time to draw a map service in ArcMap than the original .mxd map document it has been based on. The matter is that there is a longer chain of actions being involved: ArcMap needs to ask ArcGIS Server to retrieve a certain area of the map service, ArcGIS Server goes to the file geodatabase, retrieves the data needed in the extent, compiles a raster image and sends it back to ArcMap. The extra time required to get the map documents served drawn in ArcMap comparing to drawing the original vector data is something one has to accept. The only exception I can think of when the published map service will actually draw faster in ArcMap then the original .mxd document, is when the original map document contains lots of advanced symbology and multiple layers and the map service has been cached. In this case, it might go faster to get the cache tiles from the server rather than draw "raw" vector data from a geodatabase.
As a common practice, you don't need to access the map service in ArcMap if you have access to the original map document. The whole point of publishing a map document as a map service is to make the map information accessible to non-ArcMap users or users without access to the original map document.
