Depends on what screen protector it is. The cheap ones you get for 99 cents obviously won't, most don't even cover the screen completely. I've used power support screen protectors as long as I had my 4 and never broke my screen yet I have dropped it on numerous occasions, all on hard surfaces. Never seen a member on macrumors with a decent screen protector shatter their phones.
I have a feeling that the cheap ones and the expensive ones are the same. Some company in China makes them all and some companies sell them for $1 and others sell for $10.
Suckers buy the $10 ones.