Oh no, it's much simpler than that I guess. There's already a state "Playerspectating". If you're subclassing the playerclasses, all you have to do is make the player go there after he dies (from the Dying state) and add a check for the fire button in that state, just like the Dying state.
If you're not subclassing the player (which is always better), things might get a bit tougher. Your best bet then is to add a Mutate command to your mutator that respawns players, as this allows the player to view others as well. If you're making a gametype, you can still use Mutate commands, because gametypes have their own mutator. In that case you'd have to subclass DMMutator, and change you GameInfo's MutatorClass to contain the new mutie.