Probably yes. But both pets being unconscious at that time, as it was explained to me, it made zero difference.
The first one, a cat , I went back in after she died to collect her body and take home to bury in my backyard.
The second one, a toy poodle, I did leave as they were doing a cremation, paw prints etc. He wad truly sailing on a cloud when I left. The vet in question I had known since he was in high school. I trusted him completely to give my boy a lovely exit.
Toy poodles half brother had died at home some six months prior. I had planned to put him to put him to sleep in the morning but he took matters into his own paws so to speak. He was wrapped up like a burrito in a blanket all night and was ok as long as I didn’t put him down. I buried him myself the next morning. Saw no point in dragging his body to get to be cremated. Told to illustrate I don’t shy away from the moment of death when the dying being is still aware.
There are all kinds of ways for pets to exit this world. As long as they were totally unconscious I see no problem in not being there for the final shot.