If not illegal, doing that at least raises the possibility of litigation issues. Google sells the right to use its service in more or less (mostly, less) the manner I think you've described, at http://www.google.nl/enterprise/csbe/index.html.
For the free useage case, read big-G's terms of service for their CSE, and, more particularly http://www.google.com/coop/docs/cse/branding.html.
Update: As to being an "add-on" to Google's traffic -- "traffic," per se goes on the cost side of the ledger; bandwidth isn't free.
The extra traffic may translate to higher ad rates, someday, real-soon-now or in-the-sweet-by-and-by, or to more click-thru payments. But even that doesn't mean the add-on traffic will be a net economic plus for Google.
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