Yes you can include a wide range of attributes in a mosaic dataset and then control what is returned using them. In the mosaic dataset you can add additional fields, just like you add fields to a feature class. In the Properties of the Mosaic Dataset then ensure these fields are included in the 'Allowed' list. When you publish the service you will then see these fields listed in the Service Directory. There a various ways you can then interact with the fields. You can define a query to get all the attribute information and also use 'where' clauses and/or mosaic methods in the Export. As an example specifically for this being done with elevation data. Look at the WoldElevation Services. You will need to register to the WorldElevation Group on ArcGIS online, which will then give you access. In the group there is a silverlight application that show how images services can be queried and locked to specific rasters if required. These services link to elevation.arcgisonline.com/arcgis/rest/services. Using REST, queries can be made to the service to get attribute information. You can use the to define 'Where' clauses as well as using the 'ByAttribute' Mosaic method to have the imagery ordered by specific fields. On larger mosaic dataset be sure to Index fields that you intend to query frequently on.
