Not a UC'er, but another homebirth mama who couldn't catch. In fact, it is helping me process my DD's birth to read this thread bc I REALLY, REALLY wanted to catch. I'd envisioned catching my entire pg and my MW was fully supportive. Had a fast (~2hr) fierce labor, MW arrived ~3mins before babe was out. I was all positioned (on DH's lap, hanging off the side of a chair) to catch. I touched her head as she crowned, and MW and DH encouraged me to reach down and catch her as I pushed her body out, but I just couldn't. I don't know how better to explain it. My brain and heart wanted to, but my body just wouldn't go thru the motions to reach down. At the end, I asked MW to catch and hand her to me. I don't know, had I been alone, I would hope I would have been able to make my body do it.
My DD did have a tight nuchal, and the MW slipped it off as she was born. I hope someone can answer you about that question, bc i don't know.
I found this link with some various posts about nuchal cords and checking for the cord. An interesting start. http://www.gentlebirth.org/archives/nuchlcrd.html
I tend to think in the 'I can't catch' scenario that if no one were around you wouldn't have been in that position in the first place and likely would have positioned yourself closer to the floor/soft surface instinctively.
Obviously I think that there are exceptions every once in awhile but I think they are very uncommon.