When I worked at Warmoth, we had a beater guitar in the office consisting of a soloist body, strat neck, schaller mini locking tuners, corian nut, floyd bridge.
With a straight string path to the tuner post, and a well performed professional setup, it can work flawlessly. This particular guitar got lots of wammy abuse & stayed in tune flawlessly.
As I said above, the straight string pull, and a well performed professional setup work hand in hand. Part of that setup involves a very well prepared nut. If these processes are not performed with each other in mind, desired results can be reduced significantly.
With that being said, I've played EB/MM JPM's that have stayed in tune flawlessly, and some that could not stay in tune at all, same with Ibby Jems.
Best advice if you plan on having any type of floating trem (with or without a locking nut) , have it professionally setup if you are not skilled & experience to do it yourself.