In the film, he certainly didn't care.
He seduced Perry and betrayed him. He deliberately lied about the title of his book (as telling Perry the truth would have shown he was much less sympathetic than he was). He also refused to help Perry get a new lawyer for his appeals (as he wanted their execution for his book's ending).
So he lied to get close to Perry to help write his book.
This seems to echo real life. The Guardian had an article on the film where they commented:
The powerful scene in which the betrayed Smith yells at Capote,
"What's the name of your book?" is based on a letter the real Perry
Smith wrote to Capote on 12 April 1964: "I've been told that the book
is to be coming off the press and to be sold after our executions. And
that book IS entitled 'IN COLD BLOOD.' Whose [sic] fibbing?? Someone
is, that's apparent."