That seems to be an open question. Hawking radiation is not charged, but it also turns out that there is a maximum amount of charge a black hole of a given mass can have, and the lower the mass the lower the maximum allowed charge.

So it would seem that a charged black hole would evaporate by Hawking radiation until it reached the point where any further mass loss would put it over the charge limit. Physicists don’t think it is then simply going to stop radiating, and so what happens then is I believe still quite open.

There was an article in Quanta a few months ago on this: https://www.quantamagazine.org/black-hole-paradoxes-reveal-a...