helps a lot IF (a) the NSA can't eavesdrop at the backbone routers that your search request, and the reply, go through between your computer and the search engine, and (b) the NSA can't break SSL encryption.
How likely is it that SSL encryption is vulnerable? Your favorite search engine will easily turn up lots of things like:
And furthermore, SSL doesn't do anything about hiding the fact that the search request and response were with your IP address. As soon as you click on that "pressure cooker" link they know it's you anyway.
Using Tor (https://www.torproject.org/) might help. IMO you've got far better privacy using Tor and google (assuming you don't log in to google, of course, and assuming you do everything else over Tor as well) than using Startpage without Tor. Maybe even better using Tor + Startpage but I don't have any particular reason to trust or to distrust the people who run Startpage -- they may be on the level, or it may be an NSA project in disguise, for all I know. Better the devil you know than the devil you don't know, I figure, and google's search engine is far better.
If I had anything I wanted to hide from the NSA I'd be using Tor, on an old laptop, running a special linux distro, etc., because anything short of that doesn't really buy you anything. I guess the same lack of trust would apply to Tor, but you've got to start somewhere, and Tor is open source so that makes it a bit less likely to have a back door. Actually the more I think about it if I really wanted to hide anything from the NSA I wouldn't use the internet at all, and I *certainly* wouldn't be posting here. :-)