Can I silent-install 0patch Agent and have it automatically placed into a selected 0patch Central group?

(Note: this is an Enterprise feature.)

Yes. One of the arguments recognized by 0patch Agent installer during silent installation is AccountKey. You can use your Account Key, obtained from 0patch Central -> ACCOUNT, to have the agent registered to the root group of your account in 0patch Central. But each group you create in 0patch Central also has a Group Key (displayed under the group name in 0patch Central); if you provide the Group Key as the AccountKey argument, the agent will be registered directly to the chosen group.

Please refer to 0patch Agent User Manual, section "Silent Installation and Auto-Registration" for more details.