I don't think anyone is going to be able to give you a definitive answer.
Nobody has tried it to the best of my knowledge.
In theory it would work.
The important things is that the range of resistance the Happ wheel reports from all the way in one direction to all the way in the other must match what the Logitech PCB is expecting pretty closely. It's more than just using a potentiometer of the same value. You may also have to adjust the amount of travel the Happ wheel has.
Some wheels also have some type of sensor to show that the wheel is centered. If the xbox wheel has one, that would need to be fitted to the happ wheel.
Of the people who have done this hack for a PC wheel, half of them have experienced the wheel shaking back and forth when it is not held.
What happens is that the centering feedback slingshots the wheel past the center point, then it compensates by slingshoting it back the other way.
The result is a constant shaking. The solution is to turn the centering feedback way down, but a lot of people aren't happy with the weaker centering feedback at that point.