With my limited knowledge, I say yes, Taiwan is part of China, BUT China doesn't directly mean Communist China. If I recall correctly, Taiwan is (or at least was) called the Republic of China (ROC) or something along those lines, while Communist China is referred to as the People's Republic of China (PRC). ROC occupied most of the China area for a number of years, till the civil war, but then the ROC government lost all its land based area. But what is China? China is an area of eastern Asia, and some areas are "Chinas" like Indochina (Siam/Thailand/Vietnam/Laos.. ect.), and some Areas which are claimed by PRC are not Chinese (I can't name exactly, but I beleive Tibet is not ethnic Chinese, and I think there are some Turkish areas in far west PRC). I think it is wrong to assume PRC is China, because it is only one of the countries in that area, so I think Taiwan is part of China.
-Googled form this point-
Taiwan is still known as ROC, and PRC is the name for Communist china. I was wrong about Indochina, seems it is a mix of the words "India" and "China". It was named simply to describe the area between the 2 regions, so the people their are not part of India or China. Xinjiang, and specificity Second East Turkestan Republic, are not really Chinese. They are eastern provinces (quoted as "Autonomous regions") and should not be really considered China.