The force which is needed to pull the pin out, will depend on the friction of the pin and the neighbouring material, and the surface at which the friction works. Let's assume a friction factor $\mu$ of 1, though it's probably less for plastics. That means that theoretically, just as much force is needed to remove the pin, as the force put on the pin by the spring, which is 123N(or 12.5kg) in your case, assuming the springrate is constant. If the servo has an arm of 2 cm, then the maximum force the servo will be putting on the pin, is half it's stall torque, so 4.9kg. That wouldn't be enough to remove the pin. However, if the friction factor, or the arms length is lower, it may be enough.
But I'd rather be concerned that the pin doesn't get damaged after a few times, as your servo pulls it out of the tube under force. That used to be the one lifelimiting factor in the BB guns I had as a kid. Those used the same construction as you show here.
I'd advice you to use a solenoid to pull the pin out of it's hole, it does so with enough force, and much faster than a servo, greatly reducing the stress on the pin. You can easily find a solenoid strong enough to pull the pin out.