At a high level, the answer is yes, reading Chinese and an alphabetic writing system stimulates brain parts differently. For instance, in http://www.pitt.edu/~perfetti/PDF/Reading%20in%202%20writing%20systems.pdf, it says that
Not only did results show more bilateral activation for Chinese in occipital and fusiform regions, they showed more activation in a frontal area, the left middle frontal gyrus (LMFG).
At the same time, studies of Chinese
typically were not finding the same levels of activation of
the temporal-parietal region nor the inferior frontal gyrus
as found in alphabetic reading, where both are assumed
to support phonological processes.
The paper also analyses the brain activities in Chinese-English bilinguals and language learners. Alphabet readers show Chinese pattern when reading Chinese,
The critical results for word perception areas are that English speakers learning Chinese showed only left fusiform activation for English-like stimuli, but bilateral fusiform activation when viewing Chinese-like stimuli, whereas the left fusiform gyrus showed significantly greater activation for both languages relative to baseline, English speakers learning Chinese show significantly more activation for Chinese than English in the right fusiform region.
but not vice versa...
alphabetic readers learning Chinese showed the Chinese pattern for occipital and
occipital-temporal areas, Chinese native speakers for whom English was a second language did not show the alphabetic (left hemisphere dominant) pattern for English. ... they showed the Chinese pattern of bilateral occipital and occipital-temporal activation for both Chinese and English. Thus, whereas alphabetic readers showed the accommodation
pattern, Chinese readers showed the assimilation pattern, with their native language reading network supporting their second language reading.
There has also been a paper that found learning Chinese affects math ability. (http://www.pnas.org/content/103/28/10775.full.pdf)
native Chinese and English speakers treat numbers with different cortical parts of the brain
which indicates that
different language systems, such as Chinese and English, can shape the way non-language-related content is processed.