Yes, it is a requirement, but it seems to be hit or miss if it is actually enforced. The Mexicans generally accept your registration, the receipt that comes with your license plate, as proof of ownership, so you would not have to show the title.
Having said that, it is unlikely that you will be able to cross all the borders like that. It is equally unlikely that your lender will let you take the bike on this trip, since you will probably not be able to get theft insurance on it. Your US insurance won't cover you.
I rode from the US to Panama with a guy who had a lien on his bike, and a letter from his bank allowing him to take the bike out of the country, but it was a huge hassle at every border, and I wouldn't do it again. He had to sign a letter of guaranty pledging some property against the value of the bike to get it. Moral of the story is save yourself a bunch of headaches and pay it off before you go.
Someone else is going to post and say I'm an idiot and they went with a photo copy of a cereal box and not to worry about it, but that is my firsthand experience.