If something came to me claiming to be Omega, I wouldn't have a good way of judging whether to believe it.
If I saw a reason to think about Omega problems, I would push back against the way I visualize the situation.
As it is, I've just got more sympathy with a friend who had problems with math because she'd overthink word problems.
What do yuo mean with "Omega"? E.g. Chaitin's Omega or large cardinals do not fit the remarks.
I find Omega so profoundly annoying that I don't bother with problems that include it. I know, it's just a philosophical tool, but between not believing that such a thing is possible, and believing that if such a thing were possible, I couldn't recognize it, Omega just has a tremendous ugh field. If I start thinking about it a little more, I get distracted (though less intensely-- this isn't a deal-killer) by questions of motivation. If I had that much power and knowledge, I wouldn't spend my time nagging people with brain teasers.
In any case, many people on LW do think about problems including Omega. Do you imagine an appearance for Omega? A voice?