if you are lazy go for it, is easier to change strings with looking tuners
If you have a standard or roller nut then yes, you could use locking tuners.
Locking tuners and a Floyd Rose trem could be used together. The configuration that would make sense is to have a graphite nut with locking tuners, and the Floyd. Locking tuners would do you no good if you had a Floyd nut. The only benefit to having a Floyd trem with locking tuners is that there would be no slippage of the ball end in the trem, as the string ends are locked into the bridge saddles. It would also add fine tuners at the bridge to tweak your tuning. It would be an unusual configuration, but not a useless one.
A friend of mine has a custom Carvin with locking tuners and FR.
I can not tell if it helps, but this was his choice
maybe a rational point of view is that you don't need locking tuners + locking nut...but everyone has his own preferences![]()
I think you're forgetting that the Floyd locking nut also serves to seat the strings in the nut. So the problem with the above set-up is that the strings wouldn't be necessarily be re-seated in the nut slots properly, if you should dive-bomb the Floyd to the point the strings slacken.
So, why is that not a problem with a non-Floyd trem, like you would find on a Petrucci? It's not like a Floyd is going to slack the strings any more than any other trem.
I wouldn't recommend that setup, simply because I believe the Floyd Rose double locking tremolo is the best setup for tuning stability, when the Floyd is blocked ala the Axis. I'm not a big fan of a floating Floyd.