Multiple programs at once

Yes it is perfectly possible and practical to write that kind of function into your sketch. The function would most likely use the millis() timer function inside a function you called when the turn signal inputs (left and right) are sensed in your main loop and then call your left or right blinker functions as required.

Excuse me if I don't write such a function for you but rest assured it can be done and would be a better method then using external additional hardware.

Lefty