Installing Gfi Rec In Old House Without Ground, Should This Be Done?

An equipment ground is not required for a GFI device to operate, and installing a GFI is allowed as a replacement for the old two wire receptacles, which you should have since there is no ground wire.

The GFI should come with labels in the box " No Equipment Ground" that needs to be stuck on that GFI, and any other three wire outlets that the GFI may protect.

Since you do not have a ground wire, there should be no 3 wire outlets on that circuit, unless they are protected with a GFI outlet using the feed through option, or a GFI circuit breaker.