No, map documents (.MXD) do not maintain a link to layer (.LYR) files. When a layer file is added to ArcMap, the properties of that layer are read into the map. After that point the properties of the layer are stored in the .MXD, and the map document is ignorant of any layer files that were added.
Maps are generally made up of several layers. The key advantage of a layer file is that it is a way for layer information for a single layer to exist outside map documents. A layer file has the .LYR extension and each layer file is a separate file on disk. When a layer is saved to the disk, everything about the layer is saved; for example, symbology, labeling properties, path to the data, but not the data itself. When adding the layer file to another map the layer draws exactly as it was saved.
If there are a number of existing map documents built by adding layer files, and changes were made to these layer files, updating these documents require the following steps:
1. Open each map.
2. Remove the layers that were updated.
3. Add the updated layer files to the map.
4. Save the map.