Averting your eyes means you cannot see the sea hag.
Unfortunately, it is not spelled out explicitly on the sea hag’s statblock. Fortunately, there are other monsters with similar abilities that do spell this out for us. For example, in the description of the Medusa’s ability Petrifying Gaze, we see (pun intended):
Unless surprised, a creature can avert its eyes to avoid the saving throw at the start of its turn. If the creature does so, it can't see the medusa until the start of its next turn, when it can avert its eyes again. If the creature looks at the medusa in the meantime, it must immediately make the save.
This DnDBeyond search reveals quite the handful of monsters that reflect this understanding of averting your eyes.
Further, this more detailed description of averting one’s eyes is a completely natural understanding of the English language - averting your eyes by definition means you cannot see whatever you are averting your eyes from. So in some sense, it is spelled out explicitly in the sea hag’s statblock; averting your eyes means exactly that you can’t see the sea hag.
Given the plethora of other creature abilities that explicitly state that averting your eyes means you cannot see the creature, it seems quite clear that this is also the case for the sea hag.
This ruling seems consistent with the personal opinion (not official ruling) of rules designer Jeremy Crawford in this tweet about averting your eyes from a basilisk.