that one looks like a switching power supply. I’m afraid to remember that these do not work because the circuit does not draw enough current from the PSU. Though it might be different if it supplies an all-stuffed 4 SID synth…
this alim doesn’t look like a “switching” one. If you compare with the PC ones. It is all a normal transformer with diode bridge, rectifier (one for +5v, and another for +12V) etc… I might be wrong nevertheless.
I thought the transformer looked quite “small” - on the other hand, the Atari is a relatively small computer with few components (compared to today’s machines). I’d say you just try it out and tell us your results!