Well, the point of the trap was so that they'd make things so horrible that Connor would have to give in. The expected value of giving in would be much higher than the expected value of not giving in, so...

But yes, I always did get the sense that, even if Haytham loved Ziio and was rather curious and intrigued by Connor, the Order came before all else for him. He can still mourn those lost opportunities, but he wouldn't do anything differently if it would hurt the Order.