Nope. Copy button does not appear. I can copy text that way. I can copy an existing photo that way. I cannot copy a video or a frame from a video that way. It will not select the image.
I even tried selecting surrounding text, beginning before the image and ending after the image. At that point, it looks like it has selected the text and the image. The Copy button appears, and I click it. I copy, then paste it in various locations. The only thing that pastes is the text. No image.
Weird. I tested it on my iPhone before I wrote the post. Is yours older? Mine is a 5.