Yes it does! At the end of It’s Pat! The Movie, Pat and Chris get married. The movie was filmed before that little stint in Hawaii where same-sex marriages were allowed for a while, and long before the same-sex marriage-a-thon in San Francisco this year.
Therefore, Pat and Chris must be of opposite genders. Q.E.D…
I don’t think Pat was meant to be any more offensive than, say, Lyle, the Effeminate Heterosexual. 
Why, me?
I’m just a little 'ol girl, I am.
One way to look at Pat in a positive light is that it made more fun of the people around Pat who were made uncomfortable about not being able to put Pat into the conventional ‘male or female only’ category. It showed their hang-ups when confronted with non-conventionality.
Peace.