It's hard to say without more information. When you said "mate the origin of the assembly to the origin of one of the parts", do you mean you want to Float the first component inserted in the Assembly and then mate it to the Assembly planes? If yes, and all the other components are mated to it, then your drawing views may move on the sheet, but that should be all. Again, without more information it's difficult to give a better answer.
This really looks like the same question as Drawing scrambled
So, if you move the assembly (or all the parts in the assembly), you drawing views will move accordingly.
As an example, if you shift all the parts of an assembly 4" along the x axis in the negative direction, then when you come back to your drawing, the views will shift the same amount. You just need to drag them back to their positions.
Edited line-->:Locking the view focus position might help (I am not sure though):
As for your section view:
IF the section view section line sketch is tied to something on the assembly (e.g. constrained to a centerline of a circle), then the section view should shift with the move (unless the orientation of the assembly parts changed as well, e.g. shift along x axis AND rotate around Y axis)
However, if the section view section line is NOT tied to a feature on the assembly, then the section view section line will stay right where it was in space and the assembly will move under it. Therefore, you section will no longer show what it showed before. You might have an issue where the section is no longer cutting through the assembly at all, or is suddenly perfectly tangent to an area and is creating a 0 thickness section.
Anyway, no matter what, I think, if you move the parts in an assembly, you will probably have to update the drawing.