I saw the movie twice, and I don't think the CGI eyes were convincing with Alita.
Gollum for the most part worked because he and his face was entirely CGI, however in the Return of the King Prologue where Smeagol in a montage transforms into Gollum, there was some really bad CGI eyes that look far worse than anything in Alita.
Most of the rest of the CGI in Alita was good though, which is how I feel about Alita, it was good, just not great.
Alita was 100% CGI just like Gollum.