Unfortunately, these actually might not show if the GFI is working, and might give a false negative.

If there is no equipment ground, the outlet must be labeled as such, but it is allowed by code so long as protected by GFI. However, since all these testers do is shunt hot to ground, if there’s no ground connected, it won’t work and appear if the GFI is not working. However, assuming it’s working, it will still do its job, since it they protect against ALL current leakage, and not just ones through the outlet’s ground path (otherwise they’d be pretty useless).

I had a “landlord special” where they extended an old 2 wire box with no ground, and my PC case shocked the fuck out of me after I had the carpet cleaned and was walking on the damp floor. A ground would likely have dissapated that bit of current leakage, but also a GFI would have probably tripped when I touched it. They weren’t willing to run a new wire with a ground because, unsurprisingly they were cheap fucks, but I convinced them to install a GFI for safety at the very minimum.