Do you want to put the site in read only on the user end or in Content Matrix?
There is an option to connect only to 'read only' in the connection tab at the top on the Content Matrix Sharepoint edition UI.
If you connect here then you will only be allowed to migrate out of this location and you cannot adjust anything in said location from Content Matrix.
We cannot put your site into read only on the user end with Content Matrix.
The option to connect with Read Only mode will not put SP at source in Read Only mode. If you want to prevent any changes at the source done by the end users you will have to put SP itself in Read Only mode, CM will not do so.