It would be difficult, if not impossible. Leedy lugs are really slim, and even though you could fit a regular nut inside it, it's gonna be too tight to work properly.
I tried putting a 1960's Ludwig nut in my 1920's 4-bolt lug, and as you can tell from the picture, the nut is pointing way outwards. On top of the picture you see the Leedy internal parts. Maybe if you would file the nut down a little bit to make the square part of it a little slimmer, that might work. Also, you would have to use a very short spring inside; Leedy uses a little piece of brass instead of a spring and the design is quite different from what you usually see today. If you just want to be able to play the drum, you may consider using regular screws instead of proper tension rods.