It would depend on how the air enters the intake and intake ports. Have a watch of the linked video. This is on a single carb built Ford engine (for tractor pulls) where he puts a lower filter plate on it and runs the dyno (has base measurement without filter plate, lower filter plate and with air filter runs on the dyno back to back with graphs) showing gains.
Some HP and Torque can be gained with a change to how the air flows into the intake albeit not much but a measurable difference. You really would need to put your truck on a hub dyno to see the changes you are making. Doing it wrong would give a negative impact on it.
On the older 3.0L that have the circular to oval and split back to circular runner between the air box and intake like mine and
@ericbphoto's original tube you would see an improvement with doing what
@ericbphoto did on the dyno as the air would flow more freely through the tube but again it would be a small improvement at certain RPM ranges.
The older 3.0L needs the lower intake changed over along with the upper to accommodate the larger throttle body as the upper intakes are not a direct swap. The larger throttle body's can not bolt to the older upper intake as they are part of the upper intake and not removable. This was changed through the years and made as a two piece. All this info is here in the tech sections and throughout the forums.