Yes. In a legal sense alone, I don't see why anyone could really object. As long as both parties are consenting and no one is being harmed, then why not?
I grew up in a Christian community, went to a Christian school and have a lot of very religious Christian friends. After coming out to them recently a few of them have told me, irrespective of what their religious beliefs are they have no problem with having gay marriage legalised, giving gay people the rights they deserve under the law. I wish a lot more people could be that open minded and see things this way.
PS: Cute story kitty