Did Kyushu Become the Center of Power in Japan?

No. Historically, political power in Japan has been centered in the Kansai region (Nara, Kyoto) and later the Kantō region (Edo/Tokyo).

Kyushu (the southernmost main island) was important as a gateway to continental Asia (trade, diplomacy, invasion routes) and saw early state formation (e.g., Yamatai-koku), but it never became the enduring central seat of imperial or shogunal authority.