You can test if a raster is empty by using the Get Raster properties tool. One of the property types it can test is:
- ALLNODATA —Returns whether all the pixels are NoData.
A simple model with an iterator and this tool would resolve this. The tool appears to return a string value, I have no empty rasters to test with but with a valid raster it returned the text "The raster dataset isn't all NODATA.". So you could use a calculate Value tool to test if that was the text returned, if not then run the delete tool.