I think you will have to use conditional formatting and format the control to make it look invisible (font/border/background same colour as page) because
a) there is no visible option for CF
b) you have to do this (code) in the detail format event, not open or load
c) all instances of the control will be visible (or not) because there is only one of them in reality
EDIT - re: c), I think all will be invisible if the first record satisfies the test (result is true) but perhaps the last instance of the control will be invisible if the last record satisfies the test. No idea what happens if any records in between satisfy the test. Likely all that follow a true result in the middle of the records will be invisible. You might get this to work if you explicitly make visible and invisible.
EDIT 2 - sorry, I forgot that you are already explicitly setting visible property. I tested and it works for me, so try your code in the detail format event and open in print preview
The more we hear silence, the more we begin to think about our value in this universe.
Paraphrase of Professor Brian Cox.