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Should I know this word? I will admit that I have never run across this word. Is it so rare that it is close to becoming defunct? Is this a synonym for gossamer?

Should I know this word?

Yes.

I will admit that I have never run across this word.

If you've never run across it, how is it that you are asking about it?

Is it so rare that it is close to becoming defunct? Is this a synonym for gossamer?

I don't consider it all that rare, and no, it's not necessarily a synonym for gossamer. It has more ghostly connotations.

1510s, "ghost," Scottish, of uncertain origin. Weekley suggests Old Norse vorðr "guardian" in the sense of "guardian angel." Klein points to Gaelic and Irish arrach "specter, apparition."

Tolkein's nine Nazgûl were also known as Ring-wraiths. It's a word more common in poetry than everyday speech, although it's also been in the titles of assorted movies.

While not a synonym both words share the sense of semi-transparency. Wraithlike has the ghostly analogy, and gossamer to me usually refers to some form of cloth, perhaps a silk lacy thing.

Gossamer originally meant goose summer. Etymonline confirms this. It is something like the American phrase Indian Summer, a time in the fall or autumn that is a last breath of summer. I believe the American phrase comes from the warlike Amerinds who were wont to go roving, killing, stealing and kidnapping in the fall of the year. We call the new moon in October the Comanche Moon. Anglo settlers were encouraged by Spain to live in Texas as a barrier against these Comanche attacks.

Transparently (note: a malopropism) the word gossamer came to mean cobwebs since spiders are most active during that period of the year. Thus gossamer came to mean wraithlike in a sense. Have you ever walked through dew filled cobwebs on an Indian Summer night? You might tend to think wraiths surround you.