Does Han Solo gör bara det här eftersom Leia bad honom att göra det?

Foster Novelization bekräftar det - han gjorde bara det eftersom Leia frågade.

I grund och botten, den enda anledningen till att han inte sa till henne "Nej, vilken glitterström har du sniffat?" är att han var rädd att hon skulle dumpa honom igen, permanent.

He wanted to laugh derisively. If he did, he knew she might never speak to him again. “Me? No. If Luke couldn’t reach him, with all his skills and training, how can I?”
She was nodding slowly. “Luke is a Jedi. But you’re his father. There’s still light in him. I know it.”

Detta bekräftas när vi hör sina tankar när han diskuterar om han ska konfrontera Ren eller inte när han faktiskt stöter på honom:

A chance, then, to make it back to the Falcon before everything on this planet went to hell. A chance later for another reunion, on another world. A face swam before his, its features aged but still soft, the voice that emerged from between so-familiar lips biting yet always affectionate. Forming words that lingered in his thoughts. Forming, at last hearing, a request.
A request that wouldn’t go away, he knew. It would never go away. He made up his mind. Instead of retreating, he advanced. Instead of running for safety, he took up the challenge. There was no real choice, he told himself as he advanced to the edge of the walkway. And called out.
“Ben!”