No. But you can open View - Views/Lists - ASCII Table. Scroll down in the list to the non breaking space with decimal code value 160. Select this character and click on button Insert Char or double click on the character to insert the non breaking space.

In case you need to insert often non breaking spaces into files, I suggest to create a new macro with name NonBreakingSpace and following macro code:
The space character between the double quotes at end should be the non breaking space. Your browser will copy it most likely as normal space. So you need to copy this macro code first into a new file in UltraEdit, replace the normal space by a non breaking space via the ASCII table, and then copy the entire macro code into the Windows clipboard for pasting it next into the Edit Macro dialog for the new macro.

A hotkey for quick inserting the non breaking space should be assigned to the macro, for example ALT+SPACE. The two macro properties show cancel dialog for this macro and continue if search string not found should be both unchecked for this macro.

The macro should be stored together with other often needed macros in a macro file which is configured at Advanced - Macro - Set Auto Load for being automatically loaded on startup of UltraEdit so that the macro for inserting the non breaking space is by default available after starting UltraEdit.