If you remove sort params from search, yes.
When iam searching on forum here it seems im not first one as asking but havent find any good answer.
It schould be possible to rewrite search url so just be search/searchword...
edit: find this...
If you want to hide GET variables or values you should not use GET. In GET methods the data will always be send as part of the url. If you want to 'hide' the data (or not show it in the URL) from the user you should use a POST method.