Oh my...no, Ivermectin doesn't "kill the eggs", you can't really "kill the eggs", you just flush them out and make the females sterile if there are any left. Ivermectin would certainly kill all the host parasites, but honestly, I would not have treated them to begin with if the count/load was low.
Either way, at this point the concern is Iggy, as I'm positive he is very sick from the Ivermectin. I knew that was going to happen, that stuff is so strong that it's typically only used anymore on a regular basis to treat livestock, like cattle, horses, pigs, etc. Some old-time general vets will still use it TOPICALLY to treat ticks and such in dogs and cats, but never orally, and that's why I got horribly concerned when you wrote that you were dosing his roaches and then feeding them to him. The fact that this vet told you to dose his roaches instead of giving it to him orally in a direct manner tell me that he knew very well that Ivermectin is dangerous...
Honestly, I'd be giving Iggy Activated Charcoal at this point, due to the lethargy and the
black beard. Suck up any that's left in his stomach, then give ample fluids to him several times throughout the day, and bump his temps up by 5-10 degrees.
I'm sorry this vet did this to him and to you, that sucks. He should have known better than to give Ivermectin to an animal as small as a Bearded Dragon, especially orally. I mean, this is stuff that I used to recommend to the farmers who sent their herd samples to me to test, and I would tell them to only use it topically on their cattle and not orally because there is a concern about poisoning. So giving it to a little lizard is just irresponsible and dangerous...
Was he sick from the parasites in the first place, or was this just a routine fecal that happened to show positive for low counts of them?