We don't really know whether or not they were proud to be Chinese, but we do know that the Manchus created China as the political entity and Chinese as the nationality we know of today. The term China (Zhongguo, which translates into the Central Kingdom/Middle Kingdom) had been used since the 10th century BCE, but it's meaning had always been ambiguous. For most of Chinese history, China referred to the area we would now call 'China Proper' and to the Han ethnicity. A clear example would be the Manchu translation of China. Before 1644, the translation was nikan gurun (the state of the Han people), after 1644 when the Manchus moved into China proper and established control, they adopted the term China and the translation became Dulimbai gurun (the central country). Qing emperors increasingly made use of the term China when they dealt with foreign nations and they frequently used "our China" (wo Zhongguo) in their writings. Thus, the term China began to be used interchangeably with the dynastic name Qing. Just about every treaty the Qing signed with foreign powers uses China, and sometimes they use China and Qing interchangeably. An example is the Treaty of Nanking (1842), in which the English translation uses only China instead of Qing.

The Manchus also worked to remove the Han-centered meaning attached to China. As a non-Han ethnic group, they already considered themselves Chinese by virtue of using the term China to refer to their dynasty. The Manchus expanded the scope of China to include every ethnic group under their control, and the Yongzheng emperor famously wrote: "Since our dynasty began to rule China, the Mongols and other tribes living in extremely remote regions have been integrated into our territory. This is the expansion of China's territory." (Dayi juemilu). The Qianlong emperor also wrote in 1755 that, "There exists a view of China, according to which non-Han people cannot become China's subjects and their lands cannot be integrated into the territory of China. This does not represent our dynasty's understanding of China, but is instead that of the earlier Han, Tang, Song, and Ming dynasties." With every new conquest, the Qing emperors wrote that these new territories were integrated into China.

As the Qing faced a series of political and economic crisis in the 19th and 20th century, the government began to promote the imperial ideology of China to the commoners in order to raise nationalism. Manchu and Han literati alike began to support this view of a multi-ethnic Chinese nationality, textbooks were published on the geography and ethnicities of China, and Qing subjects became known as Chinese subjects, as can be seen from these two late Qing passports - 1907 and 1910. The Boxer Rebellion, which was an anti-Western movement in northern China, included Han, Manchu, and Muslims whose goal was to support the Qing and expel the foreigners, so we see that nationalism did pay off.

Now going back to your question of whether or not they were proud, I personally believe that by the end of the dynasty, they were. At least the commoners and the literati were, but it's hard to say whether it was genuine or just politics.

Source: Reinventing China: Imperial Qing Ideology and the Rise of Modern Chinese Identity in the Early Twentieth Century by Gang Zhao

Edit: Grammar and spelling

You have to distinguish between China the state and the Chinese people. The Manchus were certainly proud to be the rulers of 'the middle kingdom'. They portrayed Li Zicheng, who had brought down the Ming dynasty, as an illegitimate usurper, with themselves having restored legitimacy and avenged the last Ming emperor by defeating him and establishing their own dynasty.

However they did not see themselves as members of the Han people (the main ethnic group in China - basically the 'Chinese people'). Throughout the Qing dynasty the Manchus took steps to preserve their ethnic identity, for example using laws against intermarriage.