The spatial reference of a mosaic dataset is specified when you create it (using the Create Mosaic Dataset tool). This spatial reference is used to manage all of the data that is ingested into your mosaic dataset. As always, re-projections are performed on-the-fly by the system.
Therefore ArcGIS handles the various projections for you.
One aspect of the spatial reference you do need to worry about it which coordinate system is specified to manage your mosaic dataset. The spatial reference or the extents of the data you are ingesting into your mosaic dataset should fall within the horizon of the mosaic datasets spatial reference extent. Any data that falls outside of the spatial reference will not display. Therefore a safe approach will be to use a spatial reference that is large- such as Mercator or WGS 1984.
Submitted by: Vinay V.