I’ve left my iPad charging for four months

Your iPad will suffer no ill effects through being connected to its Power Adapter for extended periods. Your iPad will automatically regulate and optimise charging - and will not overcharge the battery. 

When used in kiosk or PoS applications - where external power is connected for extended periods of time - the iPad may modify its charging strategy and limit battery charge to ~80% of maximum. This modified charging strategy is designed to reduce chemical ageing that might otherwise occur if 100% charge is maintained at all times.

Nominal 100% charging will be restored when a normal charge/discharge routine is restored.

Not really. Some might claim that being near the top of the charge range that long without going below is bad for overall longevity, but a lot of iPads are used connected to power for months.

It doesn't continuously charge. What it will do is charge then stop, where the level will be monitored until it reaches a certain charge level and then it will "top off" until full again. This just repeats but won't result in overcharging. The charge indicator will always indicate "100%" but it's really more going between 95-100%.