Depends on your controller. I own a few controllers that are designed to run on either 36V or 48V. I have one 36V only controller that would blow up at 48V. My BBS02 controller will run at 48V and 52V, but not at 36V.
All of my own 36V/48V controllers have been run at 36, 48, and 52V, so I know they have no high voltage cutoff. Meanwhile, they can set the low voltage cutoff properly for 36V and 48V, but not for 52V. You have to count on the battery BMS shutting down the battery if voltage gets too low.
As for the LCD, depends on that too. While icon is off on 52V, if your LCD can display the actual voltage, that should be relatively correct. I know mine show the proper 58.6V when my freshly charged 52V pack is attached.
None of my bikes have speed limiters. They go faster with higher voltage. A bike with a speed limiter might accelerate faster but then you;re stuck with max speed.