The same agency is not going to put in multiple applications for you at different airlines. It'll be one at a time. If one airline doesn't like the experience, and you get rejected nice and early then they'll try another one for you and yes you're free to apply via other agencies at this point in time though they might not like it/tell you not to.
However, the first application that results in your medical being booking will mean you are now owned by that agency/airline combination. You can forget about applying to another airline until you've gone through the rest of the process (6 months), have been rejected, then told to wait a year (CAAC won't let you re-attempt the check ride for at least a year).