Both claims are ridiculous. Have you ever met a single person in your life who was fluent or at least good conversational in Esperanto but could not speak English? To say that learning Esperanto will provide you with a solid base for learning Mandarin is about as plausible as saying that learning Biochemistry will provide you with a solid base for learning Mandarin.
Learning Esperanto might be a great hobby and way to find like minded people, but the return of investment for unrelated, completely practical pursuits is highly negative. If you want to learn Mandarin, just study Mandarin.