Old post, I know, but it looks like your daughter's phone already has an AOSP custom rom installed.
Furthermore, if she got it in China then it is likely the international version of the One S, which is NOT compatible with US-version roms.
You can check by looking at the CPU max speed. If it is listed as ~1.7ghz, then it is the international version-- the "VilleC2" or S3 version of the One S. If it is ~1.5ghz, then it is the US version.
Both versions have a subforum on XDA you can visit for S-Off, Root, Recovery, and custom ROMs (at least until those show up here). Make sure you are following instructions for the right version of the phone.
But to answer your question, yes, you should be able to completely wipe the phone and clear any "China-listening-in" software that could theoretically be installed.