It seems to work for me, Claws Mail 3.9.3 in XFCE. After enabling the checkbox, opening a menu and highlighting a menu item with the mouse and then pressing a keyboard button (tried letters, function keys, plus Shift Ctrl Alt - any 1 or all 3) assigns that letter combo as the new shortcut "on-the-fly."
Here's a screenshot of the options, and the kind of buried but very helpful text in the "Choose preset keyboard shortcuts" popup.
Is that not what yours is doing? I'm not using Unity so can't compare with it directly, do you think it's "stealing" the keypresses? Do any of the keyboard shortcuts work when no menus are open?