rango - 2:40 pm on Jun 8, 2013 (gmt 0)
Well, that would be disturbing if it did. I'm not convinced that time on site or pages per visit are used in any meaningful way by Google. The only way for them to get this data would be either via Chrome, or by snooping on your analytics. Both are things they've stated they don't do (iirc), so I wouldn't count on it.
The next metric is bounce rate, which may or may not be used. In my own experience so far, improving bounce rate has had NO impact on rankings for me.
I would suggest that what's most likely is that Google has some logic more like this:
user clicked result 1) then came back and clicked result 2) and didn't continue clicking results
downvote for result 1), upvote for result 2)
This makes instinctual sense, but I'm sure Google has a slightly less basic implementation of it than that to guard against abuse.
In your case, implementing site search should positively affect this metric so I would't think it would hurt your rankings.