Can one build a distributed radio telescope? I understand some radio telescopes are built as arrays of receivers. Could one build an array from a heterogeneous set of receivers in scattered locations? Suppose a large number of persons each operate a receiver, and data is gathered together; can it function as an array? Asking for a friend.
Yes, we can do radio astronomy with heterogeneous, geographically distributed antennas.  The VLBI is an excellent example.

Of course, the antennas have to be similar in some ways for it to work:

If the antennas are ground based, they need to be in the same hemisphere, or the Earth will prevent them from looking at the same target at the same time.
They must have extremely stable timing sources, since error or drift in the time tagging will result in dB losses for a detected signal and inaccuracies in angular resolution.
They must have accurate enough timing sources to allow synchronized collections.  The collection times need to be offset in time to account for path delays to the various antennas.
They must overlap in collection RF.  Any differences in center frequency and bandwidth will mean that some of the antennas will be picking up different signals than the other(s).  Practically this usually degrades the collection quality.
It's desirable to have similar antenna beamwidths or, again, the antennas won't all be picking up the same signals.
You need to synchronize the collectors and have accurate estimates for the distances between them.  The VLBI systems use methods described here: How are the atomic clocks synchronised between worldwide VLBI telescopes?,