TOPIC: Is it right to search on your own site?

If you've added an AdSense for search box to your page, you're probably
aware of the relevant search results it provides your users. That being
said, a few publishers have asked us if it’s a violation of our program
policies to perform searches in their own AdSense for search boxes. The
short answer is no, this activity is not explicitly prohibited by our
program policies.However, we strongly advise against using your own
AdSense for search box for a couple of reasons. First, it can increase
the chance of accidental or invalid clicks on the ads that appear on
the search results pages. Second, this will inflate the number of
queries in your reports, giving you an inaccurate picture of the
activity on your site.If you’d like to use Google search, we recommend
visiting Google.com or installing the Google Toolbar. And if you're
using Google Chrome, don't forget that you can type search queries
directly into your address bar.

Source: - AdSense Publisher Support