Will a GFI outlet provide proper protection if it is installed in an existing 2-wire, 120 VAC electrical system?

Yes. In fact code allows you to replace a 2-prong receptacle with a GFI as long as it is marked "No Equipment Ground." GFI outlets usually come with a sticker that says this.

The GFI senses faults in the grounded (neutral) conductor, not the grounding (equipment ground) conductor.