If the magnitudes of the forces are the same in the two cases, the linear acceleration would not be the same. The work done by the force would exactly equal to the sum of the linear energy and the rotational energy. Therefore its linear acceleration cannot be as much if it rotates as well.
If you prefer a quantitative result, you can decompose the force in two orthogonal components, one of which passes the center of mass. The component passing the center of mass would result in linear acceleration, while the other one would result in angular acceleration.