I think that's misusing the word "avatar," though. An avatar isn't a separate being acting as an agent of a deity -- it's the actual deity incarnated in a corporeal form. So you can't become the avatar a god if you had a previous existence as a mortal. At best, I suppose the deity could possess you, but that's still fudging the definition.
I agree with you, but it's comics, we usually let them slide in areas such as this. Marvel has been misusing the word 'avatar' since the early-1980s, or at least retconning their usage of it back to the 1970s. The intent of the usage remains the same.
Becoming an avatar (by Marvel's standards) usually means that some all-powerful cosmic entity invests some of its power into a mortal, perhaps this counts as 'possession' in their books.
That's how Dan Abnett and Andy Lanning used the word throughout their run in Nova and Guardians of the Galaxy, that's how Jim Starlin and the late Mark Gruenwald used it throughout their various series'. I'm sure there are other examples...
Adam Warlock has been repeatedly described as an avatar of life. Martyr was an avatar of Death/Oblivion. Drax the Destroyer, an avatar of life. Maelstrom is an avatar of Oblivion, Quasar was/is an avatar of Infinity. Thanos now counts as an avatar of Death. It is now 'cannon' as they say.