If you made two identical knives, and then forged the fuller into one blade, that blade would be stronger (in chopping) than the other knife. Right? I think so

I think the main purpose of the fullers was to make blades lighter while retaining their strength, so the smith would forge in a fuller and use less steel.
When I think of a fuller, I think mainly of swords, not knives. I am no means an expert on either, but I think the advantage of fullering really comes into light on large blades. The fuller would strengthen the blade for chopping actions and not prying actions.
The fuller increases the moment of intertia along the neutral axis when loaded with the chopping action, which increases the "strength". Just off the top of my head, I would think the fuller would actually weaken the blade when loading it in a prying situation.
It would kinda be like laying a 2 x 8 x 12 across two saw horses. Lay it down with the big flat side parallel to the ground, and take a seat in the middle. If you are a big fat A$$ like me, the board will flex and maybe break. Now turn the board 90 deg so the big flat is perpendicular to the ground. Again take a seat, the board will not flex, so now me and all my fat friends have a place to sit.
That is why tou see the I-beam type floor joists being used in home construction now days. They have the same strength as a 2 x 8 but are made from alot less material. The "I" beam shape has two big parts (the top and bottom flats) that are far away from the center of the beam. The moment of inertia for the beam is the sum of the moments of its indiviual pieces. So the two big flats, and the vertical part all have their own moments. Each components moment is dependent on the distance it is away from the neutral axis. The neutral axis is perpendicular to the direction of the load. So the I beam has two neutral axii depending on how you load it. One moment of inertial is bigger than the other, so the beam is stronger when loaded perp to that axis. By putting the fuller into the knife blade, you are effectively moving mass farther away from the neutral axis, making that moment bigger, and the other moment(prying) smaller.
OK, I think I am confused now, but that is not hard to do. Usually happens when I try to think. I should just sick with studying the bottom of the beer bottle.
If you all have a machinist handbook, look up moment of inertia or bending moment, they have a bunch of info on how to calculate the stuff.