It is extraordinarily unlikely the CCP could control China. None of the warlords would likely cooperate with it. You would either need the CCP to defeat the warlords and unite most of the country (even more unlikely) or have a rump central state that even has less control of the country than the Nationalists had.
Furthermore, if the CCP were somehow to be in charge, Mao Zedong would not be the leader. It would have been someone else, and Mao is merely a troublesome local boss - and therefore likely to be purged at some point.
The CCP would not be able to lead China in a successful resistance against the Japanese. Likely the CCP government is quickly crushed in battle. North China falls to Japan. One (or more) of the non-Communist warlords take control and is forced to be friendly to Japan. China is kept divided and weak.
The best chance for a CCP central government is during the Northern Expedition. Instead of Chiang crushing the Communists in Shanghai, he is arrested and then assassinated in a CCP coup. The CCP rules the KMT through a temporary alliance with Wang Jingwei, but he soon finds himself to be powerless and eventually removed. The CCP - acting through the infiltrated KMT - establishes their capital at Wuhan. They are given massive aid by the Soviet Union, but this only keeps them in power in the areas they already control. The more conservative members of the KMT split and China remains divided into warlord factions. As the central China state becomes increasingly Bolshevized, the Japanese eventually provoke a war and attack. Most of the world welcomes the move since it removes the Soviet Union's only ally.