If the frost damages or kills a plant, do the seeds that aren't ripe become nonviable ?

Yes. But your confusion comes from using the term "ripen". Seeds don't ripen, they mature. Fruit ripens. Flower seeds are mature/viable when the bloom has dried on the plant.

If you pick a fruit that isn't ripe, and it ripens, are the seeds then viable ?

Varies with the fruit somewhat but as a general rule, to be viable. a seed has to mature on the plant. But again mature/viable seed is not always tied to the fruit being "ripe".

For example, tomato seeds are mature once the fruit reaches the breaker (color break) stage and that is many days prior to full ripening.

You can find FAQs on how and when to harvest many different types of seeds over on the Seed Saving forum here.

Dave

Is the 'breaker (color break) stage' of tomatoes the same as what some people call "first blush"?

Is the 'breaker (color break) stage' of tomatoes the same as what some people call "first blush"?

Yes. There are several stages of color break but what is sometimes called first blush (blush of developing color at the blossom end) is the first stage. At that point the seeds are mature and the fruit will continue to ripen to full color either on or off the vine.

Dave

For seeds to mature, in certain fruits, they don't need for the fruit to be on the plant (after a given stage). Seed draw nutrients from the fruit itself. But it is different for seeds of flower, eg. Because in that case the seeds are in fact the fruits.