That same thing that will happen if you don’t turn your cell phone off before you pump gas.
i.e. nothing
Navigation and control electronics are rigorously tested regarding external EMI (electro-magnetic interference). Navigation is primarily GPS these days and it is pretty obvious that cell phones don’t interfere with the inexpensive GPS receivers in phones, why should they affect the expensive, heavily tested GPS receivers in planes?
The original analog cell phones had a much higher output and also caused issues with connecting to many towers at once. Aviation has always been hugely conservative so the ban lasted for a long time after it was proven to be a non-issue.
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