I believe the answer is potentially. The main things which matter in high-level correspondence chess are:
Although I don't think either of those are really relevant. The really relevant bit is (apparently) planning:
For me, the key is planning, which computers do not do well — Petrosian-like evaluations of where pieces belong, what exchanges are needed, and what move orders are most precise within the long-term plan.
(From this interview with Jon Edwards (reigning correspondence world champion) from New In Chess)
I would highly recommend the interview on Perpetual Chess podcast also with Jon Edwards which I would also recommend.
I'll leave you with this final quote, which has stuck with me for ages:
The most important game in the Final was my game against Osipov. I really hoped to win in order to extend my razor-thin lead, and the game’s 119 moves testify to my determination. In one middlegame sequence, to make progress, I had to find a way to force him to advance his b-pawn one square, all while avoiding the 50-move rule. I accomplished the feat in 38 moves, in a sequence that no computer would consider or find. Such is the joy of high-level correspondence chess. Sadly, I did not subsequently find a win. But happily, I won the Final without it!
Yes, humans still provide value. Correspondence chess players will for example read chess opening books to find if there any mistakes in that book and even if they find just one, they'll try to lead their opponent into that dubious line, which is often a mistake that computers can't easily spot. Also as a former highly-ranked chess player, I'd use multiple chess engines at the same time to compare and contrast and also I'd know their strengths and weaknesses and which possibilities to explore.
In chess, AIs are very superhuman; the best players in the world would lose nearly every game against any modern computer player.
Do humans still have something to add? The continued existence of correspondence chess, IMO, suggests that they do. In correspondence chess players have days to make each move, and play from their homes. Due to the impossibility of policing cheating under these conditions, correspondence players are allowed to use computer assistance.
You might think this would make the games just a question of who has more computing power. But as far as I can tell, that’s not the case.
What are humans adding? Low confidence, but I think it’s mostly opening prep; try to find a line that looks ok on shallow computer analysis, but where deeper analysis shows you have an advantage. The human value-add is telling the computer which lines to analyze. Since the chess game tree is so large, advice like this is quite valuable.
Proof that correspondence chess is still played: https://www.nytimes.com/2022/11/09/crosswords/correspondence-chess.html Interview with a human player (from 2016): https://en.chessbase.com/post/better-than-an-engine-leonardo-ljubicic-1-2
On the other hand: I don’t play correspondence chess, so I’m not that confident in the claims above. And some people don’t find them plausible: https://twitter.com/liron/status/1660890927920201728?s=46&t=UlLg1ou4o7odVYEppVUWoQ
Why should we care? This might provide some indication of what value humans can provide in a world of superhuman AI (at least initially).
Can anyone provide a more definitive account of what value, if any, humans add in correspondence chess?