My understanding is that if the PDF has the fonts embedded, then there'd be no problems, but if not (probably because that would hugely increase the size of the file), then you'll need to do some work to replace the 'standard' fonts.
I'd suggest searching the forum for "Chinese" rather than "CJK", but as a short-cut, take a look at
http://xp.sg/hacks/unicode-support-for-prs-505/ - Note that the info
here is also relevant as it deals with the same issue (replacing the standard fonts) but while less specific to CJK fonts, has more information about the process.
As an aside, please note that an "eReader" is a quite different device to a Sony Reader!