Ahaha! Found in Infoworld Vol. 10 Issue 1 (January 1988)...
Headline: “RUNNING OS/2 ON THE MAC II: DO USERS CARE?”
Choice quotes: “The Mac 286 has everything necessary to run OS/2, but we haven’t tested it” ... “If a guy’s already got a Mac II, the idea of running OS/2 is pretty ludicrous.”
There was a Mac86 board with an 8086 processor that fit the SE/30’s PDS slot, but I’m pretty sure OS/2 1.x required a 286.
You might be able to install OS/2 on a Mac II with a Mac286 NuBus card, but it seems like a stretch. I can’t find evidence of anyone having done it.