I presume there will be opposite movements of the charged particles inside, with collision energy being exhaust as heat.
On the other hand, such a setup would probably introduce an extra noise/voltage fluctuation immunity, would also greatly simplify the circuit layout, would enable short-term high current anytime (i.e. motors, stroboscopes etc.).
Can I simultaneously charge & discharge the battery? Might it cause any harm to it?
No, you cannot simultaneously charge and discharge a battery. The net current through it will do one or the other, but not both.
The real question is, can the charger simultaneously charge the battery and power the load? That depends on the design of the charger and the nature of the load, neither of which you have provided.
You seem to be concerned about high-current short-duration loads, in which the battery would switch from charging to discharging and back again. This should work fine, as long as the charger itself is properly current-limited in order to prevent damage to it. When the load switches on, the battery will make up whatever current is needed beyond what the charger can supply.
Also, such load impulses may confuse the end-of-charge logic in the charger (assuming it has that kind of "smarts"), so you'll have to take that into account in the design of the overall system.
No, you can't charge and discharge a battery simultanously.
However, it is very common to have things connected so you appear to be charging and discharging at the same time - as in motor vehicle applications.
With the battery, charging source, and load all connected in parallel, if the load demands less current than the charger can supply, the excess current from the charger will go to charging the battery.
If the load demands more current than the charger can supply, the battery will supply the extra demand.
The switching between charge and discharge happens automatically as the available charging current and load current demands change.
