Just wonder if I can put on my blog " Find a distributor in your area" with the adsense search, would that be allowed?
It's a grey area, open to interpretation so I wouldn't risk it without official clarification. For the purposes of the AdSense terms and conditions I'm sure search boxes are considered just the same as any other ad unit, which you can only label as 'Advertisements' or 'Sponsored Links' or phrases very similar to those. However AdSense for search boxes require 2 actions on the part of the visitor for the publisher to receive payment (perform search + click sponsored search result) so are less prone to the fraudulent activities that the AdSense TOS try and legislate against. A grey area - like I said. I wouldn't use this label until I'd sought official confirmation and you can't get that here at DP.
Contact the Adsense Team. Nice guys there who usually replied within 2 to 3 days (including weekends).