Quite possibly. The classic nuclear weapons did their damage mostly through heat and pressure. They were relatively ineffective against troops in armoured vehicles, which is why alternatives like the neutron bomb were developed.
That said, the Hiroshima bomb was small by modern standards. A single Minuteman III missile can carry three W78 warheads, each with a yield of ~340 kT. China has similar nuclear capabilities.
It would be an unmitigated global catastrophe if those sorts of missiles started flying. Nobody would be safe.
