The answer is yes....depending.
An '84 to '86 SVO mustang beat one and is easy to modify as well, but costs a bit to purchase because they are pretty rare. In the early 80's they made carbureted turbo mustangs and in '83 and '84 i believe they had fuel injection but only 140 horsepower for the non-SVO mustangs.
As for the run of the mill 2.3L mustang, don't waste your time or money. A mustang, although pretty light in general, is too heavy to easily move a 2.3L mustang even one with a turbo has to spool up to get moving. You need the torque of a V8 to really move the car.
Another option you have is to get an '87-'88 Thunderbird Turbo coupe, which is a "fox" chassis car like the mustang and accepts ALOT of the mustang bolt-on parts. Other plusses is that it has decent gears (but not enough if you want to really have a revving powerhouse turbo), 4 wheel disc brakes, lots of options, (leather seats) and should easily be moddified to kill everyday ricers.
The reason why the ricers car can even move is because they have lower friction engines that are basically designed to have a powerband higher in the rev range, as well as the fact that the 4 cylinder is the "most powerful" engine in that car, whereas in a mustang the engine was mostly a stop-gap emissions and gas mileage measure to boost sales and maintain their emissions status. Good luck on whatever you decide,
------------------
Mustang Parts Specialties ripped me off, it could happen to you as well.
'84 Mustang 5.0 LX
my LX
'89 Mustang GT
my GT