Apologies for the double post, but I just passed this part again, and I don't think Verin ever really bought into the whole thing and only joined to save herself and create something that would last beyond her death. She planned for this when she saw the signs the Last Battle was coming and...
I discovered in a reread that she asked Sorilea for something to help her sleep. She was given it with the warning that too much would kill her. I think with the Last Battle coming, she knew her information would be needed so the tower could be whole.
I think Jerron has a good point. We knew from the first time we met her that Verin is curious by nature and a Brown through and through. I believe she did go undercover and did what was necessary to learn everything she could because of her pursuit of knowledge. Don't forget that Moiraine...