It would, but along with the turbo + supercharger (was running twincharged), comes the exhaust system, and to get it to idle right i ended up having to remove all but one of the cats, and even that got switched to a high flow, and there in lies the issue, you can, for certain cars (and the 86) usually get away with removing the manifold cat (as I do with the tomei uel), because it's all tucked away behind the shielding, and as long as the car still passes the sniff test you're good, but for the other exhaust sections, it has to pass both sniff test and visual inspection, which includes counting the number of cats versus OEM.
In addition to that any aftermarket exhaust parts need to be fitted with a certification plate to show that it meets a particular standard, all mufflers/exhausts without this plate fail by default, then theirs noise level tests, height from asphalt tests, all manner of test, it gets crazy and unless you put the car through yourself you're at the mercy of whether or not the inspector got out of bed on the right side that morning (so I always put them through myself)
That combined with an equal level of strictness throughout the testing procedure, coupled with the long standing government incentive and general trend to get a new car every 4-6 years means craploads of engine/car exports that in great condition, and a constant influx of cash to the government and manufacturers. People who buy one car and stick with it for 10+ years are few and far between.
But my main reason for pulling it all out and considering an engine swap is that I've pushed the FA20 to the raggedy edge and far short of making it dangerously unstable or putting serious money into major rebuild work there is little more I can do with it as it is, so my options where : undo everything and bolt it all back in after Shaken, leave it all on and just fork out the extra charges for modified vehicles (and still have to worry about failing), or just bite the bullet and make the most of modified vehicle status and go the whole 9 yards, because one of the biggest changes that occurs when your car is given modified vehicle status is, it's resale value plummets insanely, to a point where it's worth less than half the current value if selling at auction or through a dealer.
So a big, beefy engine and a much more solid transmission are future additions, with the sale of the current FI parts and eventually, the stock engine and transmission fueling the swap + rebuild, so all in all it shouldn't really be too expensive all said and done (may even make a small profit on the switch).
tl;dr Shaken sucks if you like to modify your car.