No, I don't have greyhounds. I worked in the vet business for 10 years before coming to FL and my dog groomer here is very much into greyhounds. I need to call and make an appt for my girls tomorrow (2 Cavalier King Charles Spaniels
and 1 shihtzu) and plan to ask her about it.
I don't think she would freak over being put into a crate. I'll ask Terri (groomer) about that, but most dogs love to have a place of their own to get away from it all. My shihtzu is afraid of the crate that the Cavaliers use, which is good because it gives them a place to go to get away from her when she gets rowdy (she's just a year old and they are way to dignified to play!).
I'll get back with you after I talk to my "local expert".