1. The link you provided is about LWM2M Security Object, not about how the mbed client connects to mbed Device Connector (https://connector.mbed.com/).

2. To get a better feeling on how a device would actually connect to the server, here's an easy to follow example: https://github.com/ARMmbed/mbed-client-linux-example - this can be built & run on an Ubuntu machine. (Note: there are some prerequisities, as explained in https://github.com/ARMmbed/mbed-client-linux-example/blob/ma...)

3. You can see in main.cpp (https://github.com/ARMmbed/mbed-client-linux-example/blob/ma...) that we're using certificate mode (line 128), and that's also on free accounts