I know this is not a SCIENTIFIC test with control groups and such, but I will share my thoughts on this matter and how I've been pickling my fresh egg surplus for over 25 years with absolutely no ill effects, or refrigeration.
I may add that my 4 children were raised eating these eggs, even in the hot Southern summers, and they are all very much alive with children of their own... and for me, that's proof enough of my method...okay, my deceased wife's method... and no she did not die of food poisoning.
After the obvious hard boiling and peeling of the eggs, ensuring that the egg didn't get marred or damaged, I put them into sterilized mason jars, with sliced jalapeno, chili or habanero pepper rings.
I then boil about 2 cups of pure white vinegar with a 1/4 cup of pickling salt and one 500 mg, generic white vitamin C tablet until all solids are dissolved.
I then pour it right up to the top leaving no air space, so that when the lid and ring are put on and tightened, the excess is forced out. As the jars come to room temp, the lids will emit a "POP" when the suck inward. If no "POP" is heard and the lid does not get sucked in, those jars go in the fridge, the others go in my pantry... That's it.
I have never had a jar fail, however, there would be a simple way to know if it did and you have bacterial growth, the liquid will cloud up badly, the lid will swell and in drastic contamination, will leak... but that has never happened.
Remember this, from a chemistry standpoint, bacteria is more likely to grow in sugary environments, and there is little to no sugar in my method, plus the capsasin in the peppers is highly acidic, as is the ascorbic acid in the Vit C.