Does it matter how you order your tug-of-war participants?

Yes, if you put the strongest people in the back the rope will be straighter, making it more likely everyone is pulling in the same direction.

Think of how much horizontal force you can apply. The puller, is leaning horizontally, and pushing (at an angle on the ground), and vertcal forces and rotational torque must separately balance. The more the puller can lean backwards, and the lower the rope, the more horizontal force he can apply. Presumably he can lean more, and get the rope lower from the back of the line.

I can see two advantages:

1) the more heavy set the stronger the muscles, so it means a lot of the force is coming on a long arm. The tug is supposed to be linear but rotations will happen, and there will be amplification of the effect as a lever arm. If the rope were solid this is obvious.

2) Think of two people of equal weight,on a see-saw. The one with the shorter distance from the fulcrum is at a disadvantage and has to put in more force to swing. A tug of war has a "fulcrum" at the center where the two teams meet. Putting the heavy players at the end will shift the centre of mass towards the end and will give an advantage in the impulse transfer by a longer distance from the center.