For example, if the static friction threshold was broken but then the applied force was lowered below it, would the object keep accelerating?
The question states that a force is accelerating the object to the right, does that mean static friction is irrelevant in every case? The applied force in the problem was less than the max. static friction, but once again, it was stated that "a force is accelerating the object to the right". The kinetic frictional force was well under the applied force.