Matt is quite right and if you think about this logically, what benifit would you gain at run time by placing a value into the query string of the current page? To do this would imply that you already know the value so pushing it up into the query string is a moot point.
I think the issue you are having is a logic question whereby if someone enters your search page and the value of your QueryString is an empty string you want some default text supplied so your app does not crash (or something similiar) is this correct?
If that is the case a simple test against the value can net you that result:
If Request.QueryString("Search") = "" Then
'Do Something Else
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