[EdKiefer]

Adding a turbo to a NA engine can increase its mpg, but that depends on the fuel metering system you use as to how much you'll see .
Even at idle speeds the turbo is spinning at like 20k rpm providing turbulence and the back pressure is nill on turbo at low speeds cause you can free the exhaust from turbo back (you don't need much of muffler) .
I have added turbos to few cars and it can improve overall but that also depends on how you drive of course .
You will see improvements if the vehicle has a carb or throttlebody injection with turbo downstream as the intake impeller breaks up the fuel droplets .
On modern port injection it would probably depend on how emission/fuel injection system is tuned by OEM .
If turbo is sized right even part throttle gets boost without being in boost conditions .

PS: Also you don't want to bias use/need a wastegate with turbo setup .If you try to setup turbo size so boost spikes high and needs wastegate early on then you probably will not get much improvement in mpg .
When I added turbo on my Opel 1.9 I first had it setup so card size limited boost (this is done with larger exhaust A/R housing (0.40) . Then I later went to 0.25 housing and a wastegate and while boost response was better at lower end it did eat a little mpg so how you set things up and size things has a big factor on how it affects driveability and mpg .