There's no way to really know. Relations between the upper Roman elite, and boy servants, occurred all of the time, and since it was normal, there likely wasn't anything notable in any records. It would be like "Constantine has sex, like tens of thousands of other humans." It would be a non-issue. It's only recently that we've begun to document the mundane things in life. Back then, parchment wasn't cheap, and any non-major moment of life simply wasn't recorded.
If Baba's talking about Carlos/Dual, who had a dual going as Constantine over at TK... then yes, gay.
If he's referring to the Constantine I'm thinking of, the only time he got sex from her was when she was planning on getting pregnant. Any wonder he wandered?
