Every rifle recoils straight back. Regardless of what stock is on it. The recoil impulse is always in line with the bore.
What moves the rifle are the reaction forces at your shoulder. If the shoulder is in line with the bore, the reaction is 1:1 with the recoil impulse in line with the bore. If the shoulder is lower, the reaction will always have a rearward component and an upward component. If the shoulder is higher, it will have a rearward component and a downward component. The distance lower or higher determines how the reaction forces are split, and therefore how much muzzle jump you see.
Whether or not the muzzle rises is dependent on if the upward force component is strong enough to overcome any resistance (you holding the forearm, the weight of the rifle, etc).
Jeremy