Nope. Even though you must supply your address in the registration form, a WHOIS request for your locality domain will only show information about the registrar.
This is definitely not true for general .us domains.
I registered one a year or two ago. And assuming my normal default Whois privacy was being applied (I clicked through too fast. Wasn’t paying attention)
I noticed my mistake after the spam bots started hitting me up for their web design products.
That was clearly not true for domains directly under .us when I last read their rules, roughly a year ago.
I suppose it might be true for .city.state.us subdomains, but those fail my first criterion (they're not short), and are themselves a privacy hazard since they substantially narrow the search space for personal info about the domain owner. So it doesn't refute my criticism.
Will WHOIS requests leak my address?
Nope. Even though you must supply your address in the registration form, a WHOIS request for your locality domain will only show information about the registrar.