snowfalcon2;
will the improved glide rate allow the aircraft to glide a longer distance until it meets Mother Nature?
In this circumstance, no, it will not.
This is not about rate-of-descent (except for the initial transition), it's about glide rate.
It is
indeed about rate-of-descent. There is NO room in this scenario to discuss "glide rate". By the time any meaningful "glide rate" could be established, they would have touched down, likely on the roadway.
Retracting high-lift devices, (in this case, flaps), reduces lift and would have very likely caused an earlier touchdown even with an increased pitch attitude - the near-instantaneous problem faced by this crew was balancing the available energy from the mass (the airplane) with the need to maintain an angle of attack which would accomplish this purpose but not stall the aircraft.
They would know instinctively, (to use up bandwidth in repetition) that retracting lifting devices would require an increase in the angle of attack to retain the same vertical path, (FPA - flight path angle). They would not know their stall speed nor their angle of attack (no need for either, in normal airline operations) so they would be flying on experience for the few dozen seconds they had to assess and respond to the unfolding emergency.