I believe what you are describing is a sleeve, but when you say “silicone extender” I think of a penis shaped toy that you insert into to become bigger via said toy. I’m going to forget you mentioned “extender” with my answer.
These are used to prevent chaffing of skin when PEing. They also have been mentioned to prevent turtleing after PE. I believe they work at both. On their own I don’t believe they have any merit making your dick bigger. If you are hanging, these might tear and are expensive. Most folks use Theraband it seems for this. If you are pumping hard and/or using too large of tube, I can see a sleeve reducing the fluid build up and limiting negative PI’s. Using one for stretching seems entirely odd to me. If you using are a extender, like a X4 type or similar, a piece of sleeve where you attach yourself in is almost required, or something at least to protect your skin.