Has anyone added this, and does it change your sound at all?

Or, how do you keep your guitar in tune after using the tremolo without it?

Welcome.

I've done it many times. It marginally changes the sound of any string you play open.

As to your second question, this has been discussed here ad-nauseum. Essentially, the bottom line is this: You can tune your guitar in such a way that you can really get on your non-locking tremolo and your guitar will stay in tune but when you choose to solo, the guitar will go out of tune. Conversely, you can set your guitar up in tune for soloing but if you really get on your non-locking tremolo, the guitar will not return to tune. Consequently, these are the chief two reasons why Mr. Floyd Rose is a multi-millionaire.

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