Do you know where the water is getting in at? I see that it’s coming out from the grout. If I understand the situation correctly, all that re-sealing that hole on the outside will do is make it so that the water sits inside the framing. I wouldn’t plug up the outlet hole until you’ve made sure that no more water will get in there.
ETA: As far as sealing it goes, I’d personally just smear a bead of silicone across wherever the water is getting in/out from. Grout can be a bit tricky to patch and blend, in my experience.