If the headset battery is healthy then it should show a full charge, yes.
Mind you, I don't know how often the indicator is polled or if the device needs to be switched off then on for it to update. It is also possible that the device only reports certain percentages (almost empty, roughly half, not quite full and full for example).
If the headset is new, ask about a warranty replacement. If it is old, it is possible that the battery percentage needs calibrating.
It will almost certainly be a Lithium battery of some type and the majority of devices with lithium batteries have some sort of battery monitoring and will turn themselves off to protect the battery when it gets really low.
I would run the headset until it turns itself off due to the Low Battery state then charge it up to full in a single go without interruption. This should recalibrate the battery levels in the headset.
The headset may also be charging the battery up to "almost full" then applying a tiny trickle charge to slowly crawl the rest of the way to 100%.