Yes. You are correct. This is called sympathetic or preemptive launch and is included in nuclear policy/strategy.

Essentially if you launch something towards the US or especially Russia and people don’t believe it’s not a nuke they then have to decide if they launch towards the launcher or their closest rival/enemy and those launches trigger other launches.

Most nukes are in known places in hardened bunkers or silos or better at sea in a long haul ICBM sub. If you don’t use them you lose them because they’re 100% gunna get destroyed if you don’t.