It would have been an uncomfortable conversation but far less violent if Harry told Ebenezar before working him up into a rage. Telling Carlos about Thomas would be an improvement over Harry's canon approach of clamming up when asked about his sex life, working with Lara and seemingly sneaking off to have sex with her and then refusing to give answers again when asked about that.
I don't know, it would have been more than an uncomfortable conversation. Eb got worked up just at the sight of Thomas, then the idea of little Maggie living with her father totally set him off. The revelation about Thomas was just the cherry on that huge pile of poop. I don't blame Harry for being pissed and clamming up about who he had sex with. "Talk to us, we are all friends here...." So without his permission, he is scanned to prove he had sex with somebody, the Wardens assume the worst, hell yeah, that pissed Harry off. As Chandler hinted,
"we are friends, you aren't included in that." Again, there is no way to explain about the illusion of sex with Lara, and then that Thomas is in fact his brother that is going to go down well. In a perfect world, perhaps.. But remember the tracking dot? The was the first shot of mistrust across Harry's bow, no, it would be dumb to talk to a so called friend who did that.
Harry's reasons for keeping the relationship between Thomas and himself secret has been repeatably gone over in the books. And the theme again gets raised in Battle Ground. He Who Walks Beside used the relationship to attack Harry through Justine. I'm assuming that Beside has the same or better ability as has Anduriel. I take this from Titania's warning to Harry in Cold Days. Telling Carlos represents an unacceptable level of risk. There is a movie interpretation of this type of ubiquitous surveillance, called The Conversation.
Before Cold Days even,Harry didn't have a name to put on it beyond "Black Council. But by the time that Peabody was exposed, there was ample evidence that the number of people on the Council Harry could trust was very small. At this point beyond, Listens to Wind, Rashid, and Eb, I don't think there is anyone that Harry could trust completely.