Site search can be a good thing and it can be a terrible thing. Here are some things to consider:
#1 Why do you want site search?
If you want to give a better user experience then go for it. If you want to give the false impression that your site is large and professional, don't do it. If users enter keywords that return bad or zero results this will backfire.
#2 Why do you need site search?
Do users have a problem finding your content? Is it because your pages are poorly interlinked and organized? If that is the case then you need to fix your internal links which will have the side effect of helping search engines crawl and rank your content. If on the other hand you have 1 million pages that are perfectly interlinked, then go ahead & add a search box to help users deal with the massive amount of great content.
ps: be careful about valuing the bounce rate and time metrics too much