Games : Baton Pass question

Im working on a little strategy to make my Mega Gallade a tank and Baton Pass plays a huge role in it. But i was wondering, if I use Baton Pass with one pokemon to a second pokemon and the second pokemon uses Baton Pass, will every stat increase still be passed on? For example, I send out Blaziken first and use Protect which guarantees one speed boost. Then i use Bulk Up and take a hit, and speed boost comes again. With +2 speed, I baton pass to Togekiss, which ends up with the +1 Attack, +1 Defense and +2 Speed. I use Agility and get another +2 speed, making it +4. I then take a hit, but then Baton Pass to Gallade. Would Gallade still have the +1 Attack ,+1 Defense and +2 Speed from the Blaziken? And say I use Togekiss's Baton Pass AGAIN and pass it to Umbreon and Umbreon uses Swords Dance and Agility and Baton Passes to Gallade. Would the chain of stat increases continue? Im sorry if im being stupid and theres an obvious answer to this.