Yup, they all have the same 9-pin connector. Joysticks will work a treat on all three platforms. Mice however are a bit different; Atari mice need to have 2 pins swapped for them to be usable on an Amiga. A lot of 3rd party mice of that Amiga/Atari era have a switch on the bottom to select Atari or Amiga.
Dunno if {bleep} like lightpens/guns etc will work though.