As of 6.3 you can click the "Approve" button in the Client Review Site to approve a Version. This checks the "Client Approved" field on a Version but does not currently generate a Note. We've heard feedback that it would be helpful to see this as a Note in Shotgun so it appears on the Activity Stream.
Please add your support to this feature request if you'd like to see this developed in the future.
*A current workaround is to add the "Client Approved" field as an interesting field on Versions from under the Admin Menu > Global Following Settings. Any changes to this field will then appear on the Activity Stream.