In theory you could do interferometry with a lot of orbiting radio telescopes. I'm no radio astronomy expert, but I can see a lot of practical problems with this idea.
For one thing, if you want the same signal-collecting power as the Arecibo observatory, you need dishes with the same total area. Since Arecibo is 1000 feet in diameter, if you put dishes on every one of the 12,000 satellites in the initial Starlink constellation, they would each have to be over 9 feet. That's about the same size as the chassis of the satellite itself.
In order to do anything useful with the collected data, the receivers need to have very precisely synchronized clocks, and their relative positions need to be known to within a small fraction of the wavelengths you're interested (which for Arecibo can be on the order of centimeters). I'm not sure whether GPS receivers alone would be enough to meet these requirements -- you might need to add atomic clocks to every satellite as well.
Now you have to think about how to aim the antennas. Presumably you can't just reorient the entire satellite, because its main job is to keep its ground-facing antennas aimed at the ground and its solar panels aimed at the sun. So you need to add a separate antenna pointing mechanism, with a fairly wide range of very accurate movement along multiple axes, so that all of the radio antennas can observe the same region of the sky simultaneously.
Presumably the Arecibo telescope itself is connected to fairly sensitive, low-noise, specialized signal processing equipment. You would have to take all of this equipment, design a space-rated version that can fit on a satellite, and then manufacture 12,000 of them. You also need to add enough solar panels to power it.
All of this would add a huge amount of mass to every satellite, which would make them way more expensive to launch. Note that this applies to to both the monetary cost and the opportunity cost of SpaceX's annual launch capacity.
Finally, the Starlink satellites have a roughly 5-year design lifetime, so it's not enough to build this colossally expensive telescope array once; you have to keep building and launching half a dozen replacements per day for as long as you want to continue using it. There's no way it would ever be cost-competitive with a ground-based observatory.
It's serious question, from the future.. (but no answer and downvoting - what's wrong ? I know Arecibo is very important)
..about radio telescope arrays, computer power and feasibility. Astronomers complain that they lost the sight of the stars because of Starlink. Could it be somehow compensated by an array of moving, smaller radio telescopes in orbit?
Britannica: 'The world’s most powerful radio telescope, in its combination of sensitivity, resolution, and versatility, is the Very Large Array (VLA) located on the plains of San Agustin near Socorro, in central New Mexico, U.S. The VLA consists of 27 parabolic antennas, each measuring 25 metres (82 feet) in diameter. The total collecting area is equivalent to a single 130-metre (430-foot) antenna.'
