Conte has not come close to proving he can win CL. He had a great team and couldn't make it past the group stages. Plays incredibly outdated football and so far has not shown any willingness to adapt.
So from what I see, no. He hasn't proven himself capable of winning CL. You can say Di Matteo did, but by that account any coach can win it if they get lucky. He might get lucky and win, I'm not doubting that but as far as his coaching capabilities, I do not see him leading a team there. Di Matteo's team wasn't even his, he was just a substitute coach.