Let's suppose we had to convert a commercial aircraft to an all electric craft tomorrow and use all the available parts, batteries, thrust devices and airframes becoming available, as well as take off and land on conventional runways, with a typical payload etc, would this thing fly?
This amount of specificity makes what would normally be pretty silly into something that can, if only just, work for a question.
The best aviation-specific electric engines are only somewhat heavier per unit weight (but much less powerful in absolute terms) than the best turbine engines, and will make up for it in using bus bars and distribution boards instead of extensive fuel piping, heating and pumps.
You could not simply stack a lot of small electric engines under the wings, as that would ruin the aerodynamics - the wing couldn't produce any lift due to fast jet air flowing under it. It would either have to be an all-custom design, or the engines would have to replace the turbines directly. Such engines are not currently available, but, with superconducting rotors and stators, are potentially achievable within the next decade.
Per calculations done here based on the Breguet equation, a perfect electric airliner will fly up to 10 nmi for each 1% of its weight that is dedicated to the battery. More precisely it's 9.9 nmi at a 0-100% discharge cycle with 100% efficient fans. A more realistic but still optimistic number is 7 nmi, with less than perfect fans and allowing for a 20%-95% cycle that accounts for degradation and emergency reserves.
At takeoff, the A380 can carry up to 254 metric tons of fuel, but that would only leave 44 tons for the payload, supporting up to 400 passengers, and its maximum landing weight would require less than 100 tons of fuel aboard.
Assuming the hypothetical electric 380 is reinforced for a MLW equal to MTOW (575 tons), and counting on savings from general modernization and removing the fuel system to absorb that reinforcement weight, a more realistic battery weight is 230 tons, allowing for a 68-ton payload, supporting the usual 600-passenger capacity. This makes for a 40% battery weight, and thus approximately 280 nmi or 520 km operational range.
So the short answer is: if electric engines with similar power and size to the Trent 900's cores can be produced, the airplane will fly, but its operational range would be just ~500 km, less than 4% of what the current A380 is capable of.
Practically, you would not use an A380 to fly short distances, due to its complexity in ground handling of the two flight decks. There was the Boeing 747SR, built just for the Japanese domestic market, to save on airport slots. The largest plane you'd use has to be something versatile and quick to load and unload, such as the A350 XWB.
But there are short routes for small aircraft 1that are simply begging to be electrified, and if the legacy factor and lack of infrastructure don't interfere, they likely will.