I think that makes logical sense. I was thinking of having swipe navigation options that you describe, but no back/forward navigation buttons in the web site/application itself. I trust users know how to use the back/forward buttons built into mobile web browsers as the other option for navigation.
I want to see if others were thinking the same way, or if there was some actual user behavior research on this.
Also, swipe is not really an accessible action. Screen readers (probably?)* can't tell if that touch-screen action is available for navigation. The way I think about swipe is that it is an additive navigation option, rather the default.
* I have not tested this; it's pure speculation at this point.