Rose
"Does this mean that if we sent out a probe to the edge of the observable universe that it would register another portion of the universe..."
Yes, but to make things simpler, let's suppose that the probe is already there at this very moment, at a point on the edge of the observable universe. Its view would still be confined to a sphere of radius 13.7 billion lt. yrs., but it would, indeed, be a diferent sphere. Our galaxy would not be observable, because the spacetime seen from that distance would still be that which existed shortly after the Big Bang, before our galaxy formed. Nothing could be seen beyond that location. Looking in the opposite direction, it would see a portion of the universe not observable from Earth, but which would still be limited to a view of the past extending back to the time of the Big Bang.
I know didn't I answer your question exactly, i.e., "if we sent out a probe". That's because I don't know enough maths and physics to take account of the rate of the expansion of space, and relativistic effects depending upon the velocity of the probe etc., so I hope the easy way out is OK.
"Would the probe's point of view shift so that we would eventually become unseen to it?
Yes, assuming that current theories are correct, and that space continues to expand. The probe would eventually vanish from our view, because the expansion of space would eventually result a mutual rate of recession that exceeded the speed of light.
