If I'm reading the rules correctly a running play uses up two time slots. Considering if one does not use time outs, a half could end before you complete four downs? A complete game could conceivable be just six turns?
How many turns does a normal possession last?
While it's theoretically possible that a game could only have 6 plays, I've never seen it in play or simulation and never had it reported as a play test result.
I would say that a normal game will normally have around 10-11 downs. A heavy blitzing or running game might be 8-10 plays. When two of my play testers that focus on the passing game face off against one another, the games usually have about 11-13 plays.