Invisisble fencing can be great for some dogs. My neighbors use it to keep their Boston Terriers in a 2-3 acre area. The thing I don't like about it is that dogs with a strong desire to get on the other side of the fence (as we all seem to agree a sighthound will have) will get "punished" for trying to get back into their area. Of course this is only if they are wearing the collar. You have to let them wear the collar, or any electronic collar for that matter, for quite a while so they don't associate that they will only get corrected when they are wearing the collar. I suppose you could only puy it on when you let them in the yard, but then you aren't training them to stay in your yard. I do like the way it gives a warning to let the dog change its mind about getting closer to the off limit area.
I too find the rescue workers suggestion a little off the "normal" train of thinking that most sighthound people seem to have. How about fencing in a smaller area with higher fencing until the pup is out of its puppy and adolescent stage? It makes walking your property a whole lot nicer too when you don't have to worry about stepping in anything. My dogs have a small fenced in area attached to my house and that's where they are let out to do their business or hang out when I can't have them running loose, but they still want outside.

Fred