I know very little about Falcon's.
I know the Atari Falcon has 31KHz VGA out mode similar Amiga's dblPAL/dblNTSC and so it will work (to some extent) without a scandoubler.
Not sure if it also suffers from the same problems as Amiga (i.e. games and demo's dont run in VGA mode).
The CoCo scandoubler will work with anything, but it's 16-bit.