Veganism is a philosophy about animal exploitation. Vegans don’t even eat honey because it is an animal product. If you eat eggs from a back yard chicken, you are still participating in the exploitation of that animal and feeding systems which further exploit animals. Some detailed further reading:
https://theminimalistvegan.com/backyard-eggs/

So no, a vegan would not do this. Though, what OP said about nomenclature remains true - some people are loose with the terms

e: a word