"So I think another level would be required to level the gun and then use the bore sighter to level the scope. If the bore sighter has a leveler. Is this correct?"
I believe you have an erroneous view of what a boresighter really is and what one does, most people seem to expect far more than the tool can do. I know of no boresighter that includes any means of leveling a scope. They are only meant to allow the user to get on paper, usually at 100 yards, pretty quickly. After zeroing, the optical types have a projected grid pattern which can then be used as a quick field reference to check for gross changes.
To "level" a scope, put it on a rifle with the rings loosely held and positioned for correct eye relief. Holding the rifle in a sight-vise of some type, place the rig on a bench and level the rifle in the vise. Find some absolutely vertical or horizontal line down range. Twist the scope body until the cross wires match the "target" and tighten the rings.