Would finding E.T. change our view of God?

The following is a comment I made on an article addressing the question in the title of this post. The question has been posed for a while (I hesitate to say "millennia") and much effort has been spent anticipating humanity's reaction to the discovery of extraterrestrial intelligence (ETI). But I seldom see opinions discussing the alternative. So here's my two cents:

Humans may be going down a road with the destination forever far in the distance with this question. If we find ETI (or they find us), great, the question is answered. Chat show pundits, theologians, atheists and philosophers are in business for life (to paraphrase Douglas Adams).
On the other hand, what if we don't find ETI? When do we call it quits? At what point will we say "Yes, humans are alone in the universe"? What if the time comes when we've colonized every habitable planet in the Milky Way galaxy and still haven't found life? Right now, we look at the billions of stars out there and think "Surely, someone else is out there." But if humans are ever spread across the whole galaxy (unlikely) and no one else is there, will we say then that we're definitely alone or will we look to the trillions of other galaxies, each with billions of stars, and think "Maybe they're out there?" and devise ways to investigate that possibility? Given the virtually infinite size of the Universe and possibilities of life to examine, it seems that if we don't find other intelligent life, the search could easily continue till we die - all of us.
If you've ever looked for something that wasn't there (but you didn't KNOW it wasn't there), when do you stop looking? You looked under the bed, in the fridge, between the cushions and in your pockets. And later, you looked again in all those same places and some new ones, didn't you? Even when you said to yourself "I quit!" the question still gnawed at you. Where could that thing be? The same goes for the search for ET. Even if humanity, as a collective, "quits" searching, someone will still be wondering what else to try.
Until definitive proof is found that there is ETI out there, it seems that humanity's search will continue. If that search takes however many billions or trillions of years the Universe has left, I don't doubt that there will be someone who keeps searching.