Most likely. As another poster pointed out, what this shows is that our reason--given time to work--can override more instinctual desires to cheat. Part of rationalizing is considering situations, real and unreal, that may influence the outcome. E.g. I may be being observed and if they think I am cheating they may discard me from the pay group.

Without that time you wouldn't consider that "chosen at random" may be a lie. So, to the automatic mind your odds of getting paid are the same whether you pick 3 or 6 but the reward for lying is significantly higher. A simple heuristic the automatic mind may use would be (roll)x(payout): 6 x 10 = 60 vs 3 x 10 = 30

I'd be interested if the money incentive might have influence lying in the other direction, however. E.g. I did roll a 6, but if I say the maximum number they may not pay me; if I say a lower number they may be more likely pay me. This could lead to a new rational heuristic including a chance of being paid: 6 x 10 x 0.10 = 6 vs 3 x 10 x 0.50 = 15