Sadly, no. With almost any vibrato bridge, when you change one string, it will change the position of the bridge, and you'll have to retune all the strings several times to find the bridge's new home position.
Can you detune a Floyd Rose?
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Adjust the tension screws (the ones that hold the springs - you have to unscrew the cover plate in the back first). You'd have to turn em counter clockwise. Tune your guitar. Repeat adjusting screws and tuning until the Floyd Rose tremolo is aligned with the body.
What order do you tune a Floyd Rose?
In other words, tune the strings as follows: G → D → B → A → High E → Low E. For now, it doesn't have to be perfect and it's probably better to leave a little slack since the clamps at the locking nut will also tighten up the strings when they're secured. Please note: New strings fall out of tune quickly at first.