Yes.

There'll be a text adventure community playthrough on this forum next year.

Yes, they are adventure games.

I played Thaumistry: In Charm's Way in a playthough at AG about 7 years ago, and it was great fun! It's the only text adventure I've played so far, but I'm open to trying another.

Oh yes, text adventures are without any doubt adventure games. They are just as diverse as graphic adventures and have evolved a lot since Zork, so modern parsers are excellent. See ifdb.org for an amazing database and much more. I discovered interactive fiction in 1986 (first Magnetic Scrolls and later Infocom) and still play one or two games a year. We had about a dozen community text adventure playthroughs at the old Adventure Game forum, where anybody could post commands and only one person actually played the game and posted the game's responses to everybody's input. Great fun. We played some very good games, like Spider and Web, Anchorhead, Lost Pig, Bureaucracy, Counterfeit Monkey.

Absolutely. It's right there in the name, "text adventure", and the graphical ones are descended from them. Before the graphical ones existed, we didn't even need to distinguish "text" adventures from anything else. They just were what adventure games were. (You're aware of the ur-text Colossal Cave Adventure aka ADVENT, I assume?)

Do you consider the absence of graphical representation to be key?

Key to what? To being classified as a "text adventure"? I suppose so, but I'm a bit confused about the question. Are you asking whether games that use text parsers for input and text for description, but have perhaps static (rather than animated) graphics, are "text adventures"?

Yes, and Anchorhead is one of the best adventure games I've played in any form.

Yes, and I have very found memories of playing text adventure games on the old Adventuregamers forum.