If The Thing is an cellular imitation, could it theoretically produce spawn with other organisms or imitations?

Branching out here from a different horror franchise that was heavily inspired by The Thing. One question has always wracked my brain, and I wasn't sure if this was already addressed in a source outside of the movie, such as from the novel, or video game, so I thought I would ask here.

If The Thing can imitate organisms down to the cellular level due to analyzing and replication, even including imperfections such as a heart defect, would this include any reproductive cells as well? Could a Thing ( if it desired so, or perhaps to hide the fact it is a "thing" ) produce a thing-child with an uninfected human, or another human imitation, if it was at that time imitating a human? Or are these imitations sterile in the traditional sense, and can only spread parasitically through direct assimilation?

I realize that this is a science fiction creature, but if it can copy the cellular structure of any organism, their memories, personality, memories, etc. and it adopts the DNA ( presumably, unless my knowledge is incorrect ) of it's current host organism, would it be possible as a means to spread The Thing further, or to establish a "Thing"-like society?