Happily, that's not the case. GFCI is the recommended way to make-shock-safe a
two-wire (neutral and line) receptacle even when there is no ground wire available. There's little
labels supplied with the GFCI so you can tag those outlets as not-grounding.
So, a short extension cord, with a GFCI on the end, is a worthwhile precaution
if you have two-wire or ungrounded (or just uncertain) power outlets.
"Irrelevant" would have been a better word selection than inoperable since as you say the GFCI does permit shock safety for a 2-wire system. The GFCI is based on a simple differential amplifier that confirms that what current travels in one leg also occurs in the return leg, with the concept of "ground" an electric safety architectural presumption such that if there is a difference between the differential inputs, the current difference must have found another path, and that path is presumed to be ground since ground traditionally presents a potential difference with respect to the "hot" conductor. In an arrangement with an iso xfmr feeding a GFCI device, a body coming across an energized GFCI load conductor and ground would not cause leakage current flow as there is no ground reference, thus the device serves no purpose.
Not always !!
Isolation transformers are available in TWO different types, either with neutral/ground bonding
on the output side, or with neutral floating on the output side. If you want shock-safe
due to transformer isolation while working on live circuits, only the neutral-floating
type is going to work for you. This item
TrippLite iso transformer has a 'N-G' output
limit of 0.5V, indicating that it has the neutral on the output bonded to ground on output (from
the third prong of the input wire). Hold the output LINE wire, touch a ground, and you get a shock.
It's confusing, and a little scary, that the 'isolation' situation is so poorly described. I've
tested both types of isolation transformers, they both DO have legitimate uses. A
three-prong outlet tester will 'fail' the isolation transformer output socket unless there's
a neutral-ground bond.