Partial answers, remaining alert for potential caveats in the question:
This is is a really interesting question! While resolution of a radio telescope array benefits from a huge baseline, the total receiving area (and received power) is just the sum of the effective apertures. Thus the name Square Kilometer Array refers to the sum of the dish areas, not the footprint on the Earth. For a single solid dish, gain scales with size squared and resolution with inverse size, so we tend to link improvements in gain with improvements in theoretical resolution. But for an array of small antennas, they are somewhat decoupled.
So say 2,000 cubes with effective apertures of 10 cm each could be thought of as providing a roughly similar area as a 3.7 m Voyager-like dish antenna.
But now you have the electronic thermal noise from 2,000 front-ends.
On the ground, to improve signal to noise (S/N) ratio for weak signals received from deep space, dishes like some of the larger ones of the Deep Space Network use cooled front-ends. For more on that, see the cool images (pun intended) and links in Why doesn't thermal radio emission from a DSN “hot dish” completely swamp the benefits of a cold LNA?.
But your cubes could use cold front ends as well, if they had some mechanism to radiatively cool without getting heat from the Sun, as discussed in Did any of Voyagers' receivers' front ends take advantage of the “cold of space” to lower noise? so the "collective noise" of 2,000 separate front-ends could be managed as well.
No physical connection is needed. Using ALMA as an example this time, once the signal is amplified above electronics noise, it's down-converted to a few GHz and digitized with a surprisingly low-resolution ADC. See Why are the ALMA receivers' ADCs only 3-bits? and these signals containing mostly noise with a trace of signal, now in digital form, are collected at a central correlator via fiber optic cables, as is of course as done at the SKA as well.
So to maintain the analogy, the swarm could use 10 cm telescopes and free space optical connections rather than fiber. No physical connection necessary.
For transmitting, if each of the cubes transmitss 500 milliWatts, that's a kiloWatt of total power!
If they are somehow able to know each others' relative positions accurately via timing from the nearest-neighbor optical link round-trip delays, they could encode phase when relaying their received signals, and phase themselves properly during transmit to emulate a giant phased array. See When is a phased array antenna not a phased array?
This does not provide the same gain as a solid dish of the same baseline, and that's because a sparse array will put a lot of energy into a plethora of weak side-lobes. Nonetheless there is some gain available by phasing the sparse array. That plus the power gain from having 2,000 separate power sources and transmitters, will likely allow good reception at Earth.
Also note that if the cubes are strung out in the ecliptic, then you only have a long baseline (and narrow beam width) in one direction. You'd have to incline them and play with the nodes and phasings to get a decent baseline and beam width perpendicular to the ecliptic.
So far I can't think of any reason why this couldn't be done with current, or at least currently discussed technology.
except: to note that the math needed to combine the signals (transmit or receive) needs a hefty numerical implementation along with accurate positions information of each member in the swarm and the site on Earth. While it's absolutely possible that the calculation could be distributed amongst processors throughout the swarm, the details of how to implement that in this context are beyond me and a single Stack Exchange answer. Have a look at the ALMA correlator for example (1, 2, 3, 4, 5, 6, 7) which is "space-like" in that the altitude is so high and pressure so low that conventional spinning hard drives don't work (no air cushion for read/write head) and cooling is a challenge.
This application would not need something as big as the correlator because the swarm is a one-pixel telescope in that it only needs to "image" it's target point on Earth, not a wide field like SKA, VLA, ALMA, etc.
And of course this swarm network (swarmwork? netswarm?) would all be maintained at a high level of security and integrity by using blockchain (humor).
note: this is 2012. The correlator has gone through one or more substantial upgrades since then, but I can't find a newer, embeddable video.
