Probably; the moon landings had the US' popularity skyrocket, firmly landing them in every history book worldwide. If they lose this second space race to China

Probably; the moon landings had the US' popularity skyrocket, firmly landing them in every history book worldwide. If they lose this second space race to China it won't undo that achievement, but it'll be embarrassing to the ego-driven people at the top right now (notably Trump and Musk himself).