Only real effect of string savers is that they help reduce fraying and wear.
Some people claim they tighten up the stringbed by a few pounds, but that depends on how many savers you install. If you only put in a few, then it won't have any effect. If you put in 10 or more, then you might notice a slightly tighter stringbed.
I like them for multifilament and natural gut strings. For other strings, I don't bother.
Lois: "Peter, I'm not wearing any panties."
Peter: "That's ok, honey. We can throw that chair out."