Well so far, in the books, Bran doesn't really travel through time. He becomes part of the weirwoods which experience time much differently than other living things. Like a big mush of past, present and future. But, so far, he's still limited to weirwood trees and I don't see how he'd influence the Mad King without him visiting a godswood every other day.
Bran causing the mad King to go mad feels a bit cheap and easy imho. But they could certainly do it in the show since Bran's powers are different and we don't know as much about Aerys as we do in the books.
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