It should not, but often does. Not in any legal sense. Most police learn to spot things that are out of place. It would be unusual for someone to be driving with a loaded gun in their lap you would agree? The why about it might take some menial investigation into the matters.
Suppose your wife was being abducted? You would have wanted the police to check that out, no?
Proxima est Mors, Malum Nullum adhibit Misericordiam