Yeah, that would do it.
You can try winding half of what I Jazz bass pickup is for each half, unless you are going to something else. My notes say 7,800 turns for a Jazz pickup, but I've also seen 8 or 9,000 turns listed.
You may also need to experiment a bit, and maybe wind the top coil more than the bottom.
I made two pickups like this. One for a Tele and one for a Jazz Bass. I haven't tried out the Jazz Bass, but the Tele sounds good, but is very bright.
This one had the magnets on the bottom of steel poles... probably not the best way to do it. Using rod magnets keeps the poles farther apart.