Nakamura on a video posted to his YouTube channel earlier today said he also thinks Carlsen would have played if he came in second in the Candidates.
His reasoning was that he and Carlsen are the two most widely known and followed active chess players at the moment, and Carlsen is not going to allow a world where Nakamura is Champion instead of him.
Nakamura doesn't seem upset or anything over not coming in second at the Candidates, which up until the last game it looked like he almost had a lock on.
The person he said is probably the most upset by Carlsen's decision is Caruana. Caruana collapsed in the second half of the tournament, which Nakamura thinks is because Caruana thought that only 1st mattered and so had to play for wins to try to catch Nepo. If Caruana had played for top 2 instead of 1st, Nakamura thinks he would have had no trouble achieving that.