That's pretty cool built into the outlet tester, and you could use the Test button on the GFCI outlet with a lamp plugged in down line. If the lamp goes off when you press the Test button, it is protected.No need to stick your tongue in a GFCI socket to see if it will protect you.
For $5 or so at Home Depot you can get one of these testers and know for sure whether an inverter's output (or any other outlet) is properly wired, and if the GFCI function actually works.
In many ways this is better than reading the manual. The manual might be telling the truth, but there still could be a hardware or wiring problem that might make the GFCI function inoperable. Always better to test, and even better to test regularly.
It is handy to have an outlet tester with you for checking Shore power outlets to be assured they are wired right before connecting to the van.
I just ordered a GB outlet tester (no GFCI button) on Amazon so I'll have one that stays in the van and the old one stays in the tool box in the shop. Ought to be here tomorrow.