Yes paying extra principal will speed up the payoff simply because you are paying the principal down, BUT you still pay basically the same interest payment as if you had never paid extra principal. Mortgages are purchased as a FIXED income instrument by investors because they know the exact amount of interest they will receive each month barring payoff. Credit cards and auto loans work on a daily balance to calculate the interest, mortgages are a little different. The only way a bank will reset that amortization schedule and reduce the payment is a recast of the loan.
I would keep a special account for principal reduction and add to it each month then when I had say 50 grand I would pay down the principal and recast unless I was making a great ROI on that account then I might just wait until I had enough to pay it off completely. Having the money in your possession, and not trapped in equity, frees you, If you hit hard times you can simply draw on that to make your mortgage payments or any other number of things, but I advise people to do what makes them sleep better at night. I prefer to be in control of my destiny, I don't want to have to borrow my equity back from the bank if I want to remodel my house, send a kid to college, or any number of other things.