Losing games to computers because of mistakes made under time pressure was probably a thing about 20 years ago, when Kasparov lost to DeepBlue after such a mistake(correction: it was Kramnik with the blunder, not Kasparov (see edit 2)). But after Kramnik's loss in early 2000s, no world champion ever tried to play against a computer (to my knowledge). Nowadays, there are computer only tournaments among programs with ratings well above 3300 (for comparison, Carlsen's peak rating was around 2880), and it is not uncommon for computers to make moves with no apparent meaning to humans.
No time limit for humans also mean no time limit for computers so I doubt any human can win a single game against a computer. Older models like Stockfish 8 depend on their computational power as it can look at several millions of position per second, Google AlphaZero managed to beat Stockfish with 80000 positions per second: they don't seem to depend on brute force calculations any more. Keep in mind that this is without any prior knowledge of openings etc, they are trained using reinforcement learning, starting from the rules of the game only. From there, they can develop their own strategies and implement them without making any mistakes. They create their own openings from scratch, so existing libraries is not going to be very useful.
I am not aware of any research on this but lack of a challenge from humans is probably enough evidence. Also, Grand Masters regularly use chess engines in their training routine to analyze positions, so there is that.
A few years ago there was a game between Stockfish against GM Nakamura + Rybka, which Stockfish won. It is possible that human GM + Stockfish might have better chances against AlphaZero in correspondence without any time limits, but we probably will never know.
Here is an interview with Carlsen after a game, very interesting to show what he thinks about AlphaZero.
Both Kramnik and Kasparov made serious mistakes in their matches against computers. Kasparov resigned in a drawn position and missed a knight sacrifice, and Kramnik missed a mate in 1.