No, this is not possible!
First suggestion: You can also search with Windows Explorer for a string in files. Well, you will get only the list of files found and not a list of lines which contain the string.
Second suggestion: You know that the selected directory is shown in the address bar of Windows Explorer. So you can simply click on the address bar which automatically selects the full directory path and press Ctrl+C to copy it to the Windows clipboard. Now you have to open UltraEdit (with a hot key like CTRL+ALT+U specified in the shortcut of UltraEdit), open the Find In Files dialog (also with a hot key assigned in the key mapping configuration dialog) and paste with Ctrl+V the directory name into the directory field.
Third suggestion: UE v12.10a has the option Use active file path for default directory
at Configuration - Search - Advanced. Enable this option. Now in Windows Explorer you can right click on any file in the directory and open it with UltraEdit. Next you press the hot key or toolbar icon for Find In Files and the directory from Windows Explorer is automatically inserted in the Directory field, because the active file is in this directory.
Last suggestion: Use a real file manager like Total Commander
which is even more powerful for a search in files than UltraEdit. The file format can be specified, OEM or ANSI, Unicode or HEX search, only files since date/time, only files with attribute ? set, search also in archives, etc.). Well, Total Commander also shows only a list of files where the string is found. But hit F3 on a file and Total Commander lets you view the file and a second hit on F3 will find the first occurence of the searched string. I use most of the time the search function of Total Commander and not the one of UltraEdit. Only if I want to edit some of the found strings manually, I use the Find In Files feature of UltraEdit.