Can a pilot take off at his own discretion?
Generally speaking a pilot can (physically) do whatever they want: ATC doesn't have a remote control. If you push the throttles forward and pull back on the yoke you will take off, no matter what mean things the folks in the tower are shouting at you over the radio.

Practically speaking doing so can get you into trouble: You may be met in the air by planes with more guns than yours, or projectiles from the ground may be fired in such a way as to intersect your flight path ("You might get intercepted or shot down by very annoyed military types.") -- even if that doesn't happen you may face administrative or civil action for ignoring ATC instructions in the jurisdiction where you did this. 



I'm not sure what the ATC policies are in Turkey, but the US FAA has a phrase specifically for this: UNABLE TO ISSUE DEPARTURE CLEARANCE. DEPARTURE WILL BE AT YOUR OWN RISK. (you'll find it in JO 7110.65W, on page 3-3-1). 

The emergency authority of a pilot is also recognized worldwide (at least in ICAO states - you'll find it in Annex 2, 2.3.1, conveniently quoted on Wikipedia), so if the pilot in command deems that remaining on the ground constitutes an emergency they can violate regulations to the extent necessary to meet the emergency (i.e. forego getting a clearance and take off even if ATC is saying not to).