No; he's taking a stand against being used for fighting only
Banner and Hulk have a complex relationship. This has been explored and developed in the Marvel Cinematic Universe:
- Avengers 1: Banner must learn to control The Hulk
- Avengers 2: The Hulk realises he's being used and that he's seen as a monster, decides to hijack his being and runs off to Sakaar
- Thor: Ragnarok: The Hulk gains his independence and learns what he likes
- Avengers 3: Banner must learn to hold his own without The Hulk
In Avengers: Infinity War when The Hulk refuses to "come out", Banner remarks:
Me and you have some things to work out buddy.
This is the clue we have toward the actual reasoning behind The Hulk's refusal to fight. Admittedly, even I thought that it was because he was finally scared because of Thanos (there were a few remarks in the cinema too "ah, he's scared"). However, Joe Russo (co-director of Infinity War) has commented recently that it's because The Hulk doesn't want to be used for fighting anymore:
I think people have interpreted it as Hulk's scared. I mean, certainly, that's not... I don't know that the Hulk is ever (scared). He's had his ass kicked before, and he loves a good fight. But I think that it's really reflective of the journey from (Thor) Ragnarok... These two characters are constantly in conflict with each other over control. And I think that if the Hulk were to say why, it'd be (because) Banner only wants Hulk for fighting. I think he's had enough of saving Banner's ass.
-SyFy, WHAT’S UP WITH THAT HULK-BRUCE BANNER STANDOFF? INFINITY WAR’S JOE RUSSO SAYS HULK HAS ‘HAD ENOUGH OF SAVING BANNER’S ASS’, 2018-05-08, by Benjamin Bullard
Evidently, Hulk and Banner complete this arc in the most spectacular manner, they blend into one as Professor Hulk.
It seems that Banner comes to grips with Hulk, and Hulk accepts Banner. This seems to have made them into a cohesive whole, rather than two incoherent extremes.
To be honest, I can't find the original source of that Russo quote, but it's been corroborated in the following articles: