Why do you think this would "remove the moral question" for vegetarians or vegans?
Being a vegan for the true moral/ethical reasons means not consuming any animal products...'tiny meat cells' from an animals body is obviously coming from the animal. The morality of being a vegan for me means that I don't feel that I am superior to any living being on this planet so the moral question is still very much in tact. And the idea that it's done through a "painless biopsy"...Last time I heard, biopsies aren't a walk in the park. Animals feel pain just like humans. There are many many vegans in the world and we don't see them falling on the ground dying from inadequate diets so its very apparent that it is unnecessary to eat animal products to sustain our bodies.
Anything relating to the use and exploitation of another living creature will always be a moral question for me. One that is very easy for me to know the answer.
If the cells are grown in a lab absent a conscious being, what's the difference between them and plant cells?