If the target is swimming - yes, i whould assume that this is like tying yourself to a rocket and using your free action to use it to move.
If i were the GM, i'd say that the mesmerist propeling the target has to make the check for the mental force, accounting his Cha(or Int) as the bonus insted of the regular Str, as he is in control of its movement, like the wood shool wizard uses his inteligence in place of strength when he uses his wooden spear school power because it is his mind that does the work.