No, I wouldn’t leave the nut unlocked. There aren’t any grooves to adequately cradle the strings, just the V shaped slots. Those V’s are intentional wide and most strings will have a massive amount of room to dance around and rattle in them until you lock them down. The whole design relies on vising in the strings. It even takes some practice to lock the strings in “just right” so they don’t rattle.
I think you would be opening yourself up to a world of noisy frustration. Plus, when it doesn’t work, you have no alternative because of the nut shelf.
You would be better off getting a machinist to make you a titanium nut in a traditional style.