My non-expert opinion is that yes, it definitely would.
I remember reading a year or so ago that an Apollo sample rock has been found to include an Earth rock - something brought to my attention by a hoax believer I was interacting with!
What mission, A14?
Yes, I think so.
ETA: Yes, definitely.
https://www.science.org/content/article/ancient-earth-rock-found-moon
What may be the oldest-known Earth rock has turned up in a surprising place: the moon. A 2-centimeter chip embedded in a larger rock collected by Apollo astronauts is actually a 4-billion-year-old fragment of our own planet, scientists say...
Sometime after the rock formed...an asteroid impact blasted it from Earth. It found its way to the moon, which was three times closer to Earth than it is today. The fragment was later engulfed in a lunar breccia, a motley type of rock. Finally, Apollo 14 astronauts returned it to Earth in 1971.
That was what the video presented, but I have some thoughts. If there were small pieces of the Earh material in Big Bertha, then to me it seems likely that the pieces of Earth by necessity needed to land on the moon while there was molten surface. Now how long after the Moon was created after an impact 20-200 million years finishing 4.43-4.51 BYA. So it could have easily been part of Earth blasted out when Thea collided and not an asteroid (semantics here), just an alternative means of transportation.
Thanks for the info, as I hadn't heard or perhaps forgotten that little tid bit from A14.