The longer range ones really can use it to increase hit probability. Or so I've read is true for the Phoenix and AIM-120 missiles, classed as "fire and forget". and the newest Standard missile uses a AIM-120 derived head with a bigger antenna. And I'm sure still depends on mid-course corrections (for that matter, I've read the current models self-destruct if they doesn't get guidance fairly soon after launch).
The AIM-120 uses a datalink to guide the missile close to the target, after which the missile's internal radar emitter goes active, and the missile locks onto the nearest target that it finds. This is because the radar on the missile is not nearly as powerful as the radar on the aircraft. So it's not truly a "fire and forget" missile, at least if a high probability of kill is desired. I believe the Phoenix is similar.
