The PRC being currently in power, they have been claiming that the CCP almost single-handedly defeated the Japanese – this I know from last year's news reports on Oct 1st 2016 when the PRC boasted its military might on national day. (I know this as I live in HK, I can find sources if you want, but I cannot ensure that they will be in English as most English-printed newspapers avoid provoking the national government.)
The opening of Soviet archives has led to research on their documents on the CCP, here is a source recently revealing that Mao colluded with the Japanese, meeting them and even agreeing on a truce: https://u.osu.edu/mclc/2016/07/02/truth-of-mao-zedongs-collusion-with-the-japanese-army-1/
A quote from the above:
Mao Zedong issued a secret order to Pan Hannian, telling him to negotiate directly with the Japanese army this time... [the Japanese Foreign Ministry’s local agency Maison Iwai] received a request from Pan Hannian, who said that “Actually, we would like to request a truce between the Japanese army and the CPC forces in Northern China.”
So my answer would be: to a major extent, but though there were strategical reasons behind their avoidance of war, the CCP was also almost incapable of waging war against the Japanese for lack of modern equipment. Furthermore, they had been holed up in the mountainous region of Shaanxi and Yan'an after the Long March, away from the Japanese who focused on urban areas, cities along the Eastern coast. To fight them would have required the CCP to deliberately treck to those areas, which would diminish supplies and strength.
However, there was still CCP fighting to a minor extent, in the form of guerrilla warfare. The following I quote from Jonathan D. Spence's The Search for Modern China: pg 461
"...since neither the Japanese, the provisional north China government, nor the Inner Mongolian Federation had complete control over [the CCP's] terrain, there was ample room for Communist political maneuvers, sabotage, and even the recruitment of new troops in to the Eighth Route Army. In addition, the survivors of the Communists forces who at the time of the Long March had been left behind in central China to conduct guerrilla actions were now reorganized as the New Fourth Army. With 12,000 combat troops, this army was nominally subject to overall Guomindang direction by was actually commanded by veteran Communist officers ... with the Long March veteran Zhu De serving as commander in chief and Peng Dehuai as his deputy commander - but also of large numbers of local, full-time armed forces based permanently in their own home areas. These local regulars were supported by militia forces of men and women aged sixteen to forty-five who held down regular jobs in farms or the towns, and were poorly armed but invaluable in gathering intelligence and giving logistical support and shelter to the regular forces."
(I selected this section as CCP "fighting" also consisted largely of intelligence rather than direct military confrontation, used for guerrilla fighting - where this counts is up to you.)
"... in 1940 the Communists launched a series of attacks against Japanese strong points, roads and railways in northern China. Called the Hundred Regiments Offensive – in fact as many as 104 regiments of CCP-affiliated troops were involved at different times – the attacks were coordinated by General Peng Dehuai ... Despite the courage with which the attacks were carried out, none of these objectives was attained. Though the Japanese did suffer heavy losses, the regular Japanese forces, with puppet troops as reinforcements, launched shattering counterattacks, often of immense cruelty, in which whole villages were destroyed to the last human being, farm animal, and building ... the Eighth Route Army lost 100,000 men to death, wounds, or desertion. Nor did events in north China stop GMD generals in central China from paying attention to the New Fourth Army. They were fully aware that the New Fourth Army gave the CCP a vital strategic presence in the Yangzi delta, which was China's richest food-producing area and the focus for much of China's heavy industry, now Japanese-controlled."
"General Peng Dehuai attempted to combat the Japanese witht he conventional techniques of modern warfare, but his forces could not overcome Japan's strength in manpower and supply ... they were in no position to act ... "