Didger 3 and previous versions cannot. However, you can get the free ExpressView Browser Plug-in (MrSID) for Windows from LizardTech, the inventors of the MrSID format. You can use ExpressView to both view a MrSID and also convert it to a TIF with a TFW world file. Didger can then import the TIF file and read the georeferencing information from the TFW world file.
Updated October 10, 2016