While those laws get annoying sometimes, without them neighborhoods have no recourse against the jackass who wants to have some 1/2 torn apart camaro sitting on blocks in his driveway while the earth slowly reclaims it as rust.
I would wait and see what the inspector has to say about a tarp. It may turn out that now that they know the car isn’t registered a tarp isn’t going to solve your problem. Had you tarped it originally I doubt the inspector would have any legal grounds for peaking under the tarp to see if the car has plates.