First, you’re arguing with someone making a joke, and second, yes, he understood the axioms very well and was able to use the system to prove his incompleteness theorems, but, citation needed on whether he actually read the full three volumes? Russell himself said that “I used to know of only six people who had read the later parts of the book. Three of these were Poles... The other three were Texans [Gödel was neither Polish, nor Texan]”