It will cost way more than the $700 upcharge GM wants for the 1.4 to turbo a naturally aspirated engine. The cost in parts alone will run at least $1500 for a base non-ball bearing turbo kit. That won't include fuel upgrades and tuning, which will have to be done as the ECU will not have the necessary programming to handle the massive changes in airflow.
On top of the cost of parts, you will never be able to push as much boost through the 1.8 as you can with the 1.4. The engine has a higher compression ratio, non-forged pistons, and a weaker rotating assembly overall. Most NA engines top out at less than 10 PSI before they will scatter parts out of the bottom of the engine.
with the 1.4 you are starting with all of that, and can easily push 20 PSI through the stock engine with no internal modifications, 20 PSI on the 1.4 will easily outshine 10PSI on the 1.8.
That doesn't even begin to take into consideration the rest of the drive line, and what it can or can't handle power wise, or the fact that there is no one offering an actual kit for the 1.8.