Generally speaking, no; however, these are really two separate issues. An officer may tow your car for an unrelated reason and then obtain a search warrant later while it's in impound.. You should speak with a criminal defense lawyer in your area.
You should be looking for a criminal defense attorney.
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The answer to your question is of course no, but I take it the officer will have a different opinion on whether there was "cause" for a search. Boyfriends that drive without licenses and have a criminal past don't typically tell their girlfriends that just got their car towed because of their actions that the officer had cause.