No! UltraEdit is a text editor and not a file manager - use your file manager. Moving a file requires user interaction because the destination folder must be specified. You can setup a user tool (VB script, batch file) which moves your current file to a folder you specify while executing the tool. It depends on your tool how comfortable selecting/entering the destination folder is. An example for a user tool command line which opens Windows Explorer in tree mode and selects the currently open file in UltraEdit:
In UE v14.10 you will be able to do such a file move from inside UE with the context menu on Explorer tab in the File Tree View because you will have the possibility to open the Explorer context menu and therefore you can use file cut and file paste.
Best regards from Austria