Closing the hatch on the SDV doesn't seem to have any effects
If you close the hatch when above water(so no water will leak), and then submerge:
-You will have watery/blurry vision if you don't have diving goggles.(Like in swimming)
-You will eventually start running out of air and die due to asphixation, unless wearing a rebreather. (And even if you do, it wont be visible although it does protect you from asphyxiation - see this issue: http://feedback.arma3.com/view.php?id=9750)
I'm not if the hatch is supposed to seal the SDV airtight, because in real life SDVs don't have hatches at all, but since we have them here, it'd make sense to have them protect the occupants from the water effects.