First, just to be clear, you're talking about an 'invisible' not an 'electric' fence - correct? I just want to make sure, because my answer would be very different.

The only exposure I've had to an 'invisible' fence was the Shepherd across the way. There are very strict covenants regarding fencing in our neighborhood, and they could not have a fence. The German Shepherd, Jasmine, did quite well with it; BUT, after the family moved away, we talked to Sharon, who owned the dog, and she discovered after they moved that Jasmine had been blind for some time and they didn't know it. It seems Jas knew the property/house so well she didn't need sight. So, I don't know how much of the behaviour modification was the fence and how much was the blindness.

Sorry; that probably didn't help much, but it's the only exposure I've had to an invisible fence.