I just changed my old google searchbox with Adsense's official search box.
This is what I found in Adsense's Terms & Conditions. Apparently I can't do that :( ....
(ii) edit, modify, filter or change the order of the information contained in any Ad, Link, Ad Unit, Search Result, or Referral Button, or remove, obscure or minimize any Ad, Link, Ad Unit, Search Result, or Referral Button in any way;
You will not modify, adapt, translate, prepare derivative works from, decompile, reverse engineer, disassemble or otherwise attempt to derive source code from any Google services, software, or documentation, or create or attempt to create a substitute or similar service or product through use of or access to the Program or proprietary information related thereto.