If your file gets loaded via one of the native raster drivers then it will not use the OVR files (if present). If it is loaded via the GDAL raster driver, then it may use OVR files. However, sometimes the overviews are not compatible with what our raster engine uses and so this may also prevent them being used.
An MRR generally has the overview data embedded in the file although it is easy to accidentally create MRR's without this data via the UI. In all the processing operations there is a checkbox for "Display Output File". If you turn this off you get no overviews.
If you load a raster of some other format like TIFF, then the raster engine will create a PPRC file which is our own equivalent of an OVR file. The PPRC file is created once - when you first open the file - and will be reused thereafter. There are some special rules in place for JPEG rasters that will prevent a PPRC being created for JPEG's unless they are very large.