I'm not sure of having understood your goal, but in my opinion your main problem is to detect if either exists or not a query string.
I think that your code should be like this
@if(Request.QueryString.HasKeys())
{
if(!Request.QueryString["searchField"].IsEmpty() ){
<p>searchField has value</p>
} else {
<p>searchField hasn't value</p>
}
}