Question about AdSense for search

[gamex]

I am creating a website which will allow users to create their own
personal page of links, kind of like a favorites menu. I want to give them
the option to add a google search bar on this page, and I was going to use
my google adsense code. However, I will not have any control over what
kind of links the users put on this page nor how many links the user puts
on their page. I know when displaying google ads on a page, the page must
have content because the advertiser is paying, and ads on a blank page are
pointless. However, since this is a search and the user will be searching
for anything, does it matter how much content is on the page with the
search bar? I mean, if a user has one link and selects to have a google
search bar, would that be a problem or would it violate googles terms at
all? What if someone posts a link to an adult site and googles search is on there, would that still count as adult content?

Thanks!