Commander personal cloak, makes commander stealthy?

Does the personal cloak prevent the commander from showing up on radar when it is active? I know in Ba/TechA, units can be cloak-able but not stealthy so there is a radar dot that shows up for them when they enter radar range, albeit the radar dot is a bit off from the unit's actual location.

Is that the same thing here? If I equip a cloaking module, is it also necessary to bring a radar jammer to be 100% invisible?

There should never be a unit in the following situation:

• Standing in LOS.
• Visible to radar.
• Not visible to sight.

Any such unit is bugged. There is possibly a small period of time spent in this state while going between states.