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Ignoring the physics entirely, politics and finance would get in the way so, no.
From the article:

"400 septillion watts per second"

... And the context is talking about solar output, not a rate of change.

Sigh.

Considering the source, I almost wish it was intentional - the science/engineering equivalent of a click bait headline.
The engineering issues are cool to think about. Setting out to build the whole sphere at once is too much of an all-or-nothing thing IMHO. Instead, build a relatively small solar satellite in orbit around the sun at the chosen distance, maybe between Mars and the asteroid belt. Then build another one, and connect them together. Keep doing that, working towards a ring around the sun. That part should be relatively simple, since each of the pieces would be in a stable orbit by itself.

If you still need more power after that, then you consider the ring to be the equator of a sphere, and start building out the rest of the sphere, one ring of latitude at a time. Maybe build it as a basic grid or something initially, and add the solar collectors as needed. The stress would probably start to get higher and higher as you built up and down, since the pieces wouldn't be in orbit anymore, and so would rely on the structure to keep them in position and connected.

The problems in getting started are probably more along the lines of needing the kind of robot technology to gather the materials and build something like the initial satellite without much supervision, being able to gather the energy, and being able to do something useful with it.

No. In even a modest(hah!)structure like Larry Niven's Ringworld the tensile strength required to hold it together exceeds that of any known material. Sorry I'm too lazy to dig up the specific reference, but I'll give you a pretty picture instead.

http://www.dennisantinori.com/Resources/Ringworld/

Edit: a reference

>>> Peter Weston passed the word from a British college professor: the tensile strength of the Ringworld floor needs to be on the order of the force that holds an atomic nucleus together. From such stuff you could make a garbage bag that would hold a thermonuclear explosion. http://www.larryniven.net/stories/macrostructures.shtml

The Ringworld only requires such enormous tensile strength because it's spun to produce gravity on the interior surface. If you don't plan to inhabit the interior surface, there's no need to spin it, and the problem goes away.

A sufficiently thin continuous sphere can be held up entirely by radiation pressure, but still presents engineering challenges with damping oscillations; a continuous structure is likely to tear itself apart just because it's practically impossible to keep everything absolutely perfectly balanced on such a large scale. Which is why, per the article, the Dyson Swarm, a sphere made of lots of independently flying satellites, is much more plausible.

Incidentally, there are ways to eliminate the tensile load on a ringworld; you "just" have to stack enough suborbital mass outside of it (coupled by maglev rails or some such set up) so that the compression balances it out.

I wonder how feasible it would be to rotate a ringworld at a speed not to replicate gravity, but to negate the sun's gravity. So at 1AU it would orbit in roughly the same length of time as Earth itself.
You'd actually want to rotate it at slightly faster than orbital velocity, I think.

Tension is much stronger than compression, especially at larger scales.

But then you don't have the "nice" way of keeping the atmosphere in.

My thought was something like a Stanford Torus, because then you could simply add additional rings on different orbital inclinations to build an almost sphere out of rings (reminiscent of M.C. Eschers drawing) and given good design you could create rings with day night cycles.
One thing the article didn't talk about in relation to the dyson swarm is that if each unit is self-contained and collecting energy, how does it then transmit that energy to ... somewhere else (presumably one of the habitation units)? Are there obvious answers I'm not thinking about for energy transmission when you don't have a physical grid of wires to move it through?
The article suggests lasers.
A Dyson sphere is a very large embodiment of a simple idea -- inside the sphere you have a low-entropy high-temperature energy source. Outside the sphere you have the ultimate heat sink -- space. All you need to do is harvest the energy from the heat source, and allow the waste heat to radiate into space.

Imagine a Dyson sphere surface, every square meter of which would have more than enough potential energy available for virtually any purpose. Imagine something crude like a steam-driven power plant. A facility at the sphere surface would heat water to steam below the surface, then drive a piston or turbine, then recondense the steam to water above the surface by radiating the waste energy into space.

Or one could use a thermocouple, not very efficient, but very reliable. There's a thermocouple power supply on the moon right now, it's been there for about 45 years and it's still going strong. The Curiosity Mars rover has a thermocouple power supply also. These devices exploit a temperature difference to generate electricity. Again, not very efficient, but reliable -- no moving parts.

> Are there obvious answers I'm not thinking about for energy transmission when you don't have a physical grid of wires to move it through?

Well, there's no reason not to have wires if that's desired. Just generate electricity in one of many ways as above, then transmit it to where it's more useful. An alternative would be to live on a moon orbiting the sphere, and radiate the power up to the moon in the form of microwaves or laser beams.