Could Geordi LaForge gaze upon Medusa, without suffering the fate of petrification?

Yes. Recall that Perseus slew her by looking at her only indirectly, as a reflection in his shield. Geordi also sees things indirectly. I would put my money on his survival in that confrontation.

I’m also bearing in mind that even Medusa’s head, parted from her body by Perseus’s sword, was still powerful enough to turn men to stone. Geordi’s not a sword guy. If he encountered her, I hope he would have his look and then exit with all deliberate speed.

If Medusa wants Geordi, Medusa gets Geordi.

Maybe not. All he needed to be is a guy I think.

I believe he could. Although, I think it’s better he doesn’t risk it.