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Assuming Lithium-Ion, Lithium-P, etc.
The charge controller in the device is normally managed by the system to provide system current demand first and the difference between that and the charge current available from the external charger diverted to battery charging. So this, for example, allows the device to start even when the battery is completely discharged. In moments of peak system demand if the difference becomes negative, only the extra required over the charger's capacity to meet the system demand is taken from the battery.
The charge controller manages the stepped charge regime as the battery charges and battery float, and may evaluate the charge capacity of the attached charger and, for example, refuse to charge if charge current insufficient or offer a display message that the charger is of low capacity such as many Samsung devices do.
I think this has applied to probably all devices for quite some years now, apart perhaps for some cheaper ones.
A common occurrence where the system uses more energy than the external charger can provide is when using a phone for navigation in a car and the 12v cigarette lighter type charger is an older on (so can only provide 200 or 500mA). In that case the system takes energy from the charger and the shortfall from that from the device's battery - until the battery is discharged.
For many years now I usually run my notebooks when in use with charger attached so that they remain fully charged. I often run tablets and phone sitting attached to a charger for the same reason.
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