If a turbo will make boost depends on three things (assuming the engine is running).
1. The size of the turbo
2. The amount of exhaust gas moving
3. That the CFM being moved by the turbo is anything greater than the amount of air being consumed by the engine Naturally Aspirated.
So if the turbo being used is small it could add boost at 1000rpm even with the throttle at 1% open. It could probably do that to about 3000rpm before one of two things happen it is spinning to fast and could kill itself using a turbo for a 1.9l 4cylinder on a 6L V8. Or using the same turbo/engine set up it could be fine spinning that fast but at 3000rpm could be the point that the CFM consumed by the engine is equal to the CFM pushed by the turbo resulting in 0 boost.
If you keep the RPMs low a set up with a small turbo could work well to improve MPG. The increase would be from being able to run at a lower throttle position in a higher gear where it would have lugged the engine if it produced less power. AKA add a turbo and much taller gearing.
If you wanted to bypass the turbo get an electronic exhaust cutout
QTP » Electric Exhaust Cutouts that will allow you to divert exhaust remotely and you could set up a controller to do it for you.
As for the comparison of one engine being NA and the same one being Turbo from the factory and the turbo not having better MPG most of the time there are a few reasons for it. On most of the cars the following things are different between the two (not all things will be changed but some); Pistons are different compression, a cam for turbo performance, gear ratio, VMC (vehicle motor control) programming (enrichment, timing shift points, torque converter lock speed,...), and they are built for PERFORMANCE HP/TQ.