Going for aftermarket oil will not void your warranty, as long as it fulfills the manufacturer's specs, i.e. SAE viscosity and API grade. The owner's manual gives you a viscosity chart and grade range for a reason.
That said, 3-4k km is a complete waste of mineral oil, let alone synthetic. Even an API SC mineral should last 5k km in a properly working FX.
Synthetic's offer better sludge control, and are less volatile; they are more resistant to heat in high speed and turbocharged applications. Your car will likely never reach those kind of oil temperatures though. Synthetics also offer better starting and performance in below freezing temperatures.
So really, the only advantages of synthetic you will get are better sludge control and longer OCI's.