Nope, you can skip fast between tunings.
For drop c for example: thicker strings are needed, the tunig is lower than standard. To keep the tremolo floating in the right position the string tension needs to be equal to the string tension in the desired tuning. If you tune the low c up to a d you break that balance and the trem will not be in the right position, the strings will detune, etc...
You would have to set the trem up for a balance with the d standard tuning whe changing the tuning. That's the one bad thing about floating tremolos. On the other sidem they never go out of tune if set up right and you can get really cool sounds from them.
Have a guitar tech set your guitar up for the tuning because it's a bit complicated to do if you have never seen it. Let the tech do it in front of you and let him explain hoe the trem works !!!
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