Well, you have to think about the logistics of remote mounting a forced induction setup.
A supercharger works by essentially sitting on top of or replacing your intake manifold. Numerous bolts attach the supercharger to the top of the engine, with gasket(s) ensuring a seal against the vacuum.
You would need to mount the supercharger (which is not a small object), fab up tubing (similar to intercooler tubing) that runs to the intake, and tubing to the throttle body. Superchargers produce a lot of heat and with all the tubing, the air would heat up quite a bit before it finally got to the intake manifold. You could add an intercooler or spray (meth, water, alky, etc) cooling, but of course that is another step and cost.
Using the stock intake manifold would limit your results even more, regardless of how much boost you're running. It isn't optimized for forced induction, much less the higher levels of air flow you're trying to run. Also, the manifolds and head design on those motors are optimized for low & mid range torque, not high end horsepower, further choking your power potential.
You would quickly push the limits of the stock fueling system as well, or be running against the top of its capacity. That means one failure in the fuel system would quickly starve your motor of fuel and start detonating. If you're lucky, minor damage and lesson learned. If you're unlucky, you'll need to rebuild or drop in a new motor.
And I have no idea how much boost the internals of the 3400 can take, but I can't imagine it will be much. Maybe you would play it safe and setup some type of wastegate to keep it at 3 or 4 psi, but after a while of that you might get bored and try 5psi. Then 7psi. Then...BOOM.
I don't mean to entirely discourage you, just pointing out your challenges. If you could do this, it would be neat. Not practical or efficient, but neat. But as mentioned in the talk about cooling and fueling, boost is EXPENSIVE. Sure an SC pulled off a junker and some tubing isn't expensive. But then you have to cool the IAT's, get more fuel into the manifold, and the price tag climbs. Let's not forget about the drivetrain too; how much torque can that old 4-speed auto take?
A remote mounted turbo would be more practical in terms of packaging - turbo's are very small compared to superchargers. Plus a lot of research and design will have already been done. But an IC and fuel system upgrades are more than likely a must. And your power gains will be minimal, and you WILL see turbo lag given the relatively small displacement of the motor compounded by whatever distance there is from the intake to the turbo and back.
A lot of people do remote mounted (in the back of the car, under the rear bumper essentially) turbo's on Vette's and GTO's (other cars too, I'm sure). But they have double the displacement pushing out of the exhaust into the turbo to spin it up. You would use a smaller turbo clearly, but thus your gains are smaller.
Here's a couple alternate thoughts for you:
*LT1 swap - yes, it requires a lot of work. Any of these options do. But LT1's should be dirt cheap these days, the hard research is already done, you just have to put the TLC in.
*LS1 swap - this is possible with even more gains to be realized, but requires more work and a LOT more cost. LSx motors are expensive and so are the parts to convert it. I heavily researched swapped an LSx into a 3rd gen Fbody, so I'm familiar with it.
An alternative here is to find a 5.3L truck motor, or the 5.3L from the Impala SS/Grand Prix GXP. These are much cheaper to find than the aluminum block LS1/LS2/LS3 motors and have similar power potential, mostly limited by the heads/intake.
*3800 SC swap - These motors should be plentiful and cheap, along with the transmissions, from the many Pontiac's & Buick's of the late 90's. The biggest concern I can think of is it fitting in the low engine bay. Again, SC's are a packaging concern.
*Treat this car like a queen, save your pennies and in a few years find an LS1 F-body. Put on an exhaust, sways bars and good tires to enjoy your ride in the meantime.
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