not as easy as that.. all tubing needs to change due to additional routing of airflow, then cooling systems also will be added (intercooler), then need to remap your car / tune it for larger horse power, and also car will be hotter overall as turbo creates alot of heat under the bonnet. Supercharger similar... basically both systems are trying to compress more air into engine cylinder to create more power.. and that creates more heat. Main difference is that Turbo uses exhaust gas to ram more air into the piston cylinder and Supercharge uses a belt driven mechanism achieve the same thing.

Lastly difference is that supercharger has more immediate response but Turbo, depending on size of turbo and also tuning. If you want maxpower, there will be a turbo lag (slower turbo response - slower pickup acceleration). If you want response, (usually uses smaller turbos - and tuned with less pressure) you will get good pick up response but no high end power.

you also have to upgrade the brakes, absorbers

Better check proper. But usually if there is a turbo charger, all the tubing will be there. Cos the car cannot function without it.

theoratically you can run without an intercooler, no issues but.... hot charged air isnt gona be efficient.
whatsmore, If its got the stock internals(im assuming high compression), you can only run that little boost before everything turns on you.

how bout fueling and the electronics? dont tell me stock too??

There is no point aftermarket BOT without intercooler.

Either the owner ran out of funds or it's not complete yet. I bet it's still running on stock ECU with stock AF map too.

yeah, if it was a completed project, the cost of the intercooler would be so little given the effort put in to bot the car. without an intercooler, you can only run so little boost. Makes no sense not to run an intercooler. 

If car originally NA then add on turbo, then you may need to upgrade radiator. Engine can get very hot hence added cooling is good.

Next is the intercooler which is a separate system from the engine. The more efficient the intercooler, the better. Also, engine oil also needs to be synthetic (as it can hold optimum thickness (viscosity) at higher temperature; plus engine oil change will be quicker (i.e. if usual oil change is 10K with syn oil, then with a turbo, you probably want to change between 5k-7k km per oil cycle. But that is only if you have tuned turbo for higher psi / bar pressure) The higher the more power, but also more turbo lag and more heat. 

Other things need to look at, are Blow Off Valves (or By Pass Valves), High Pressure Fuel Pump, Re Mapping / Tuning of Car (as you are making the engine deliver more power, hence ignition timing needs to be tuned), you may also only use RON97 if the car is running on higher compression ratios. Other things has already been mentioned like suspension, brakes calipers & Rotors, turbo timer).

Additional / optional are oil catch cans, engine mounts, LSDs, sway / strut bars (this can be important if the flexes too much during extreme acceleration and cornering).

previous and current HP diff?

upgrade brake system, good tires with better grip. (this manyak important, can fast cannot stop = gg)

Buy a stand alone ecu... get use to the ecu software,and learn how to use it. Learn basic of ecu tuning...
Then progress from there. This is my advice for those who wanna start to learn more about turbo....ecu tuning will make or blow an engine...

My 4g92p with stock internals manage to take boost up to 1bar from kul to johor none stop. My ecu is just aftermarket link atom..i learn alot from my tuner,and many thanks to my tuner who is willing to teach me too..