Well sorta kinda maybe, but not really.. long
You will not get the same results from raising the compression as turbo charging. Well you can get more power from both (turbo or increased compression ratio) but the reason this happens is different.
Why does increasing compression ratios increase HP? Not sure exactly. You aren't compressing more air you are just compressing the air you have in the cylinder into a smaller volume. This smaller volume may help produce a much more efficient combustion as the air and fuel are more tighly mixed.(spectulating)
A turbo on the other hand helps an engine breath better and increases the volumetric efficiency of the engine. Imagine a normally aspirated engine piston trying to pull enough air into the cylinder to fill it COMPLETELY. When the piston is moving slowly the cylinder fills up very easily. As the rpm increases the ability of the piston to fill up the cylinder goes down because the air must travel much faster and has much less time to enter the cylinder before the intake valve closes. Because of the resistance in the intake and the airs inertia the air will never fill the cylinder completely. This is where volumetric efficiency comes from.
Volumetric efficiency = actual volume of air in cylinder / volume of cylinder
Why turbos make power. They increase the volumetric efficiency. They allow more fuel to be added to the cylinder because more air can be added.
The piston in a turbo engine doesn't have to suck as hard to get air into the cylinder as the intake charge is pressurized and air is forced into the cylinder. Not only are you able to get that cylinder completely filled with air but you can fill it with air at a much higher pressure than a normally aspirated engine.
Atmospheric pressure is around 14.7 psi normally (sea level). When a normally aspirated engine sucks air in, the air pressure inside the cylinder at the end of the intake stroke will never equal atmospheric pressure. Why? Because the volumetric efficiency of the engine is not 100%. The cylinder will be filled with air because air is a gas but that air will not be at 14.7 psi but maybe 13 psi(speculating). So you end up with a cylinder with less air than it could have and the capacity to produce less power. New cars with 4 valves/cylinder will be able to get closer to the actual atmospheric pressure but they will never reach it without turbo charging.
Well it's way past my bed time. I didn't read this over so if it reads like crap and i mostly bull crap, well you get what you pay for and this was free.
Good night.
Jeffrey