A pump is BLOOD coming into the muscles and lactic acid buildup. If your muscles are "filled" with blood than this logically indicates that the blood is going IN faster than it can come OUT. So nothing is rushing through the muscles quickly or there would not be a pump. I.E. blood would move out as quickly as it moved in. If blood is not going out as quickly than the pump cannot cause things to move in more quickly. Most all your body's processes have to do with getting good stuff in and bad stuff out. So by that stanpoint revcovery could only be increased by relaxing the pump...which happens anyway in a quick enough fashion so as not to make any long term differences in recovery. It's all just a bunch of dwelling on phsiological details.
Stretching will do the opposite of a pump. Experiment with a light weight high rep pump producing workout and then do some light stretching and you will find that it makes the pump go away faster.
Unless you stretch so hard you are causing your muscles to contract violently against it...which is dangerous and ill founded to say the least. And a good way to end up dropping your power down the toilet. A light stretch, I think though does aid in recovery and keeping certain muscles from shortening/tightening up, etc..
If a pump has any value in terms of recovery then it would have to be a long term value based on it's affects in increasing cappilary density, etc. But that would not have to have anything to do with some little thing you did after a workout and could just as well take the form of some kind of GPP or high rep workouts that was done in place of "cardio" or what have you.
My philosophy is NOT to dwell on muscle chemistry but to worry about how my body moves and functions as a whole. So the things I do before and after a workout have that in mind. Gaining mass is easy compared to continuing to move injury free and get stronger for years on end. All these little recovery details are all of the same bag whether you dwell on post workout nutrition or some other standpoint where people go off the deep end focusing on details and imo there are better ways to spend you time. For instance, instead of random high rep stuff just to get a pump, how about high rep stuff specifically picked for a purpose, such as "prehab" or what have you. And then you might get a pump anyway, lol.
Admittedly I'm not much for the bodybuilding mindset...I don't want to work so hard for temporary gains (at least more temporary). I wouldn't quibble about the pump except to say don't over concern yourself with it.
If you want to read the science on whether the muscle pump actually ELEVATES blood flow then you can go to JAP (journal of applied physiology) and get some very entertaining reading
. It's debated but most say clearly not. I fell asleep after the first rebuttal though so don't ask me.