Adding Google search on your site help you rank more?

[bomb]

So I never understood why people add google search on their sites. It never really does a great job of searching your site. But, does it help our site in any way when someone searches from it? I just hope it gives some sort of boost whenever someone uses the search. But, does anything happen when you do?

Otherwise, I figure I may just add my own custom search bar instead.

Well, Google search is a product like any other, so it is not certain that it will increase your traffic. But i know it will make it easy for google spiders to crawl your site. When your site is crawled easily, you increase your chances of moving to the top of the SERP.