Yes, if you enable in the configuration dialog at section File Handling
- Advanced - Open from Explorer also opens files list and
- Load - Reload files previously open on startup.
This works with UE v12.20b+1, but it does not work with UE v11.20a (Win98). With v11.20a UE starts, opens the last opened project files and immediately exits when a file is specified also on the command line (= double clicked in Windows Explorer).
A solution which always works even for v11.20a is to not use the 2 options above and specify on the command line first the project file with full path in double quotes and then optionally the file to open. But this solution means you have to modify all shortcuts to uedit32.exe in LNK files and also in registry accordingly. Of course, in the registry only those open commands should be modified which does not have also the /p parameter for printing the opened file.
@="\"C:\\path to UltraEdit program directory\\Uedit32.exe\" \"C:\\path to project file\\project file name.prj\" \"%1\""
@="\"C:\\path to UltraEdit program directory\\Uedit32.exe\" /p \"%1\""