For example, if I’ve got a path with a 3px border, I’d like it to snap to the edge of the border and not to the path its self?
Here’s a square which has the path snap to the guides instead of the square’s border:
The nodes of a path will always be centered with respect to the stroke (unless when dealing with live path effects or the powerstroke, but that’s a different subject)
You might still be able to achieve what you want, but only when dealing with bounding boxes. For this, go to Preferences -> Tools and set the bounding box to visual (as opposed to geometric). You can now transform the object or selection such that “true” corner will snap to the grid.
Should you be trying to make crisp bitmaps, then you might want to have a look at the pixelsnap extension, see here.