I don't have JAWS to test with, but using NVDA and locking the left mouse button on that "URL Button" doesn't seem to have the desired effect, either. It seems to grab the screen as a whole. If I have the screen not maximized, hit the key sequence to lock the left mouse button, and try to move the real mouse the whole Firefox screen moves.
I have always found drag and drop by keyboard to be a very dicey proposition. That's one of the reasons I like the, "Copy the URL then use create shortcut on the desktop itself" method as it's foolproof for someone trying to do this strictly using the keyboard.
Brian - Windows 10 Home, 64-Bit, Version 1803, Build 17134
The real art of conversation is not only to say the right thing in the right place but to leave unsaid the wrong thing at the tempting moment.
~ Dorothy Nevill