I would definitely not use both charging options at the same time. It could be that the internal charging electronics recognise when both the quick charger and the direct 230V connection are used. However, if the internal electronics cannot detect this, the battery will be charged with too high a current, which can damage the battery.

There is no indication of this in the manual. I myself have and use only the built-in charger. However, I strongly assume that only one of the two charging options is to be used at a time.