I think it integrates fine, but there isn't anything that really connects them. Clayface the film is an origin story and by the end of the film he's definitely Clayface the villain. Clayface in Creature Commandos doesn't say or do a lot (as the Clayface persona), and we know so little about his motivation, so he is easily the same character. Both versions show a weakness to electricity, but generally any Clayface should have that weakness, but it is a connection.

In terms of a Batman reference, to pull a quote from the director,

"You're in a city called Gotham. So I guess you feel the shadow of the Bat inherently," Watkins said. "Because of the nature of where you are."

I felt the corruption of Gotham in the film. I can see a city that needs a hero. Is that Batman's shadow? I don't think so.

Plus Creature Commandos got a Batman cameo. Clayface could have had a reference. "Wayne Enterprises trying to help blah blah blah" would have been enough.