I can say I never heard of injecting fat into penises, but I would guess if that procedure actually works, it would not go away after a while (think about injecting fat into other places).
When you ask does it actually work, what do you mean?
The trend towards injecting one’s own fat in place of artificial fillers is rising because there is less chance for complications and if done right will be perminant or last far longer then other fillers making repeat procedures way far apart if any. And fat injected in the dumbstick can make a Louisville slugger into a fat bat but it won’t help with length just thickness.