I don't know too much Mandarin, but I think it makes sense for an Anglophone to study Mandarin to proficiency and then pick up enough Japanese for casual use. The characters make up a good portion of the study requirements, and many are inter-recognizable between the two languages. Also, once you've wrapped your brain around Mandarin grammar, I think Japanese grammar should be much easier to approach.

As someone who speaks both Chinese and Japanese I'm sorry to say that this plan doesn't make much sense. Chinese and Japanese grammar are structural opposites, with Chinese being much closer to English word order while Japanese is back to front so to speak. Chinese characters are used in Japanese but many of them look different due to simplification and centuries of linguistic drift. The pronunciations are also very different between the two languages so even if you can kind of guess what certain words mean you won't be able to verbalize them.

To form a crude comparison, what you proposed is like a Japanese or Chinese person talking about how they'll learn French first and then pick up German easily because they already know the alphabet.