No, not with UltraEdit without manual creation of an auto complete file.

You could click with right mouse button into the function list view, select List for all Project Files. After the list is updated right click again into the list and select Copy to Clipboard. Now open a new file, paste it and save it. Specify this file as auto complete file for files with the extension ??? at Configuration - Editor - Word Wrap/Tab Settings.

But you can see the disadvantages. The auto complete file must be updated manually whenever you add public functions and it is not project specific. Also the list contains private functions if you have not a function string definition in your wordfile which excludes private functions.

What you really want is supported by UEStudio with its IntelliSense feature.