I actually do feel it could be a huge deal.
Rational people would say it's not a big deal. But this process is totally irrational.
I wouldn't do it, unless you thought you had a better chance at matching at the place you got the interview from..
It could seriously come down to this:
Well, we have these two applicants, they're about the same.. and they both rotated here.
"Well, Johnny Q took off for an interview somewhere else.. I guess he doesn't want to come here as badly as Bobby Y. We'll put Bobby in front of Johnny."
Just think about it..If you were the people making the decision.. if you have no other gaugue to go by.. what else would you use??? eye color? shoe size?
Seriously.. it's that crazy