I just had a Mathews Center String Stop put on my new to me Mathews Denalin and LOVE it!! I added a 1 inch longer draw length cam and it gained me 10yds with my pins. I then added the string stop and it as well added 10yds to the pins, not too mention quieted the bow to the point you almost barely hear it go off in the shooting lane, indoors!!!! Even took the nearly un-noticeable recoil away. worth what I paid for it. Also got new limb and string dampeners in orange color and alternated them with the black ones to give me a Harley Davidson black and orange theme.

Second, I can understand how adding the draw length to your bow would add some distance to your first pin setting because you would be gaining some additional speed (therefore hitting higher). But if you sit and think about it - there is a good possibility that you didn't actually gain 10 yds distance. What you really did was change your string angle and the peep's relation to your eye, in effect, raising your peep sight, which would make you shoot higher. Although Shooting your bow may feel the same - except for DL - you changed the angle relationships of peep, string, sight and your eye.
But for the life of me I can't see how a string stop would increase your speed.

I didn't have to change my peep adjustment at all. I fully understand what you are saying for I thought the same thing till I went through it.
According to the shop guy, it does add speed for it stops the string oscilliations from around 35-40 per shot to less than 10. He stated that it causes the bow to vibrate/flex less thus transferring more energy to the string to the arrow. So with this in hand, why were my groups again 4 inches high after just adding the stop just like when I changed the cam?
Too much hassle to go back and then keep records upon each adjustment to verify or debunk the claim. I just know what I had to do to get things back on target after these additions.

I don't think the string stop can affect transfer of energy. The string oscillations that the stop is reducing occur after the arrow has left the bow. Quieter is better though.

String stops have been known to bring a little bit (1-7fps) of extra speed. It has to do with the string stopping faster therefore a quicker release of the arrow. Usually when we install stops here at the shop we chrono before and after and it is usually a 1-3 fps gain. the highest I have ever seen is 7 or 8fps.

Thank you.