Yes. No animal was intentionally harmed or killed to be turned into oil. This puts it in the same category as foraged deer antlers or cicada wings, or I guess compost where you found a squirrel carcass and added it to the pile.
You could argue that animals are harmed by the process of extracting and burning fossil fuels, and thus it’s not vegan. But this isn’t very convincing to me, since that’s a secondary effect and not necessary to the process of consuming fossil fuels. (Or at least not necessary in the same way that killing chickens is necessary in order to make chicken sandwiches, for example.) And if you start worrying about a big web of consequences of your actions, then it seems like you’re mostly just adding stress to your life without actually making the world a better place.
Imo “backyard eggs” are really small potatoes, especially when like 98% of eggs globally come from factory farms. But even in that case, egg-laying hens are basically bred to suffer. They lay an egg every 1-2 days, compared to like once a month in the wild, which takes a huge amount of energy and nutrients. And we’ve bred them to produce eggs too big for their bodies, so that even when they’re treated really well, the vast majority of hens have bone fractures.
That’s why animal sanctuaries will usually either feed the eggs back to the hens, or give them medication to stop them from laying at all.
Of course, this is on top of the fact that 100% of egg-laying hen breeders, everywhere, kill the males shortly after birth because they can’t lay eggs. See this for more information.