Knowledge is endless, so I’m not 
. I just happened to research the topic when I needed to select ballscrew thickness and speed a few months ago.
The formula above (for more details see here, here, here) only considers the screw length between the bearings and not the position of the nut. The calculated speed will even excite the natural frequency of the screw in the reverse configuration (driving nut, driven screw).
My understanding is that the position of the nut (as well as the time spent at the critical speed) will affect the amount of the damage. If someone can shed more light here or is willing to perform any FEA, they are welcome.
In any case, lead and ballscrew manufacturers advise to stay at 80% of the critical speed or below to avoid premature wear or failure.
EDIT:
One more thing to consider. When you hit a guitar chord your left hand is an end stop. When you rotate a lead screw the nut is not. The whole length will rotate.