Yes, You could do that, but you must consider two things
1) If the charger doesn’t compensate for the load current, the charge time is increased.
2) If the battery is very depleted i.e. < 3.0V/cell , many of the chargers use a trickle current at the beginning of charging. The trickle current is not usually sufficed to drive the load, so it must be disconnected under this phase.
Another solution is to have a power mux that connects the load to the battery or to the external charger supply.
TI, Siliconix and others makes this type of IC.
One of the drawbacks is that the voltage regulators may not be able to withstand the external voltage if for example somebody plugs in a power supply with higher voltage.