It can be left connected to ground, but it should be disconnected from the battery, otherwise you will be measuring battery voltage.
I test my 2MC by removing the fuse, and leaving the bike for a few hours, or even overnight.
I then switch the ignition on (with the fuse still removed, and lights etc. switched off) and if I see the charge light and neutral light (it's a MkIII) flash on briefly, then I know that the 2MC has held its charge.
The problem with the 2MC is that it becomes conductive, eventually, so it can cause the battery to drain. If an owner finds their battery goes flat quickly when the bike is not being used, and a 2MC is fitted, then (provided it's not being caused by a faulty battery?) try disconnecting the 2MC.