For those who don't know, Kurt did actually appear on an ECW show and it would seem was being built towards a feud with Taz. I don't think you would have seen Kurt in too many extreme matches, ECW displayed all kind of styles and I can't see them exactly putting their star man, a former Olympian into matches against New Jack somehow, it just wouldn't have worked. You'd have seen him in more MMA style matches I think against the likes of Taz and Guido, people that could genuinely wrestle until he had become a solid professional wrestler then he would have probably moved on to the likes of Rob Van Dam, Jerry Lynn etc.
Kurt would of still probably signed with the WWF, even if he stayed with ECW. He would of probably had some feuds with guys like Taz, Little Guido and Lance Storm. By the time late 1998, early 1999 rolled around. If he was still apart of ECW, I'm sure either the WWF or WCW would of showed some interest in signing him. Even if the crucifix angle never happened, he wouldn't of stayed 'til the very end of the company.
He might have wrestled 2 or 3 matches but he would have quickly figured out what kind of promotion ECW was, and he would have left for the WWF. He was an Olympic "hero" and one with a lot of potential for pro wrestling so ECW just wasn't the right fit for him.