I'd much more enjoy an NIT run, possibly to Madison Square Garden, then the first round loss that would inevtiably come if ND somehow sneaks into the NCAAs. There, I said it. I don't pretend that it would be better for recruiting. I'm just speaking purely from a fan's perspective.
Almost thirty years ago, I really enjoyed watching ND make it to the championship game of the NIT. It was far more enjoyable to watch than the string of first round NCAA losses that followed over the years. The on-campus atmosphere when it gets to be a second or third-round NIT game is really appealing, as well.