The obvious comparison to make here is to Japanese, as it's a real-life hybrid script and is currently the only non-Chinese language to use them. However, it's important to consider that Japanese did not have an existing writing system when Chinese characters were brought over, and for quite a while the Japanese elites wrote strictly in Classical/Literary Chinese, even after the evolution of hiragana (which were more often used by women).
Given that you have actual Chinese people in this exiled empire you describe, they will almost certainly be writing in Literary Chinese but speaking some form of vernacular (the specifics of which will depend upon where in China they've come from), so it's possible that Chinese characters will be repurposed to write Nahuatl, particularly if the Chinese become the dominant group in the area. Or it's possible that the opposite will happen, particularly if the Aztecs are the dominant group, and the Chinese will begin to write their language (be it Literary Chinese or their spoken vernacular) using the Aztec script.
The idea of the Chinese script influencing the Aztec script but the opposite not being likely seems to be based on some misplaced ideas about simpler characters being inherently better and more likely to catch on -- which script becomes dominant is more likely to be influenced by the sociopolitics of this situation rather than any inherent qualities of the script. Also be sure to keep in mind that different scripts are better for different writing materials -- will the Chinese be able to continue to produce the kinds of paper, ink, and brushes they're used to in the Americas? These are the sorts of things you need to research, ponder, and decide for yourself.