I does to those animals I have saved. Let me give you a couple of instances. Since I have been doing this since I was a child, I have a LOT of them, but these are recent,
Gracie (whose name I stole) was going to be sent to the pound. I happened to be at the Humane Society when she and her Spanish speaking owners came in the door. There must have been 15 people in the lobby and she ran up to me and put her paws on my knees. It was a done deal. The HS did not have room for her and they told them to take her to the pound. I opened my mouth and out came the words, "I can find her a home." I was a dead woman when I got home, or was I? I brought her home, all the way telling my husband that I would rehome her quickly. We came in the door and he was sitting in the chair scowling until she walked up to him and laid her head on his feet. He was done, too. Smart cookie, that dog. She is a yellow lab (full blood) and was already spayed. She sleeps on my side of the bed!
When I had a feral colony, I placed 20 cats in a year. I had them fixed and shots through a feral program at the HS. One woman "just wanted to try it." She came back for another cat!
So, does it make a difference? If I can save the lives of animals who cannot speak for themselves, yes, it makes a huge difference in mine and that animals lives.