The sub has a FIXED speaker level output - when you adjust the x-over on the sub, it does not affect the output to the other speakers. Most subs have a high fixed x-over point from the sub; 120-150Hz often, though some I have seen do use 80Hz. These outputs are generally intended for small satellite speakers. That means you are still at the mercy of that high pass x-over because you will have to adjust the sub's x-over to match whatever the high pass is. If you adjust the x-over lower than the appropriate blending point to the high pass, you will create a dip in your response. This is not the recommended method of connecting a system.
If you have a receiver that has bass management, that is the best choice. If you don't have a system that has bass management, I would still send a full range signal to the speakers as that would allow you to blend the sub to the mains manually giving you the cleanest blend between the two.