If, according to many of you here, Jesus being married would have no theological connotations, then why did The Last Temptation of Christ cause so much of a ruckus? If I recall correctly, Christians (both Protestants and Catholics) were angered that Scorcese would depict Christ as having lust (and sex). Presumably if Jesus was married, he would have sex, right? (Or maybe not?)
The obvious joke there is if he was married, obviously he wasn't having sex.
Seriously though, Catholic dogma would take a huge hit if it was proven that Jesus would be married. It is the foundation of their school of thought to keep priests celibate (despite the definitely non-celibate lifestyle Popes at the very least enjoyed for most of Catholic history). Because of that, they really can't play the Protestant card of "it doesn't matter." It would rock the foundations of what they base their belief system on.
I'm not a Catholic, but in fairness to them, nobody considers the celibate priesthood to be the foundation of the Catholic belief system. They could allow priests to marry tomorrow while leaving the rest of the church completely unchanged otherwise.
To be clear, I'm not attempting to be anti-Catholic. My wife is Catholic and we are raising out kids Catholic.
That said, from the Catholic point of view, the priesthood is taking the place of Jesus on earth. I don't mean to say that whether or not priests are celibate is a foundational issue, but anything that revolves around priests is a big deal. From my point of view, they could allow women to become priests tomorrow and nothing would have to change otherwise, but you're fooling yourself if you don't think that would be a major change within the church.
Catholic dogma is that it is actually clear in scripture that Jesus was unmarried, thus why they base their structure on an unmarried priesthood. The priesthood tells Catholics how they should interpret certain scripture. If they are proven wrong on one of their interpretations, they (at least in my opinion) lose their credibility to be able to interpret other parts of scripture.