I am sure IBM would be very hostile against someone distributing AIX/370 or AIX/ESA to run with Hercules, but I'm not sure who owns what remains of Amdahl.
Fujitsu bought most of the remains of Amdahl. I don't think much of the Amdahl mainframe business is left. I haven't heard of anyone running an Amdahl system in years, they'd be ancient by now and never supported 64-bit.
Amdahl UTS however ended up being supported by another company "UTS Global" (not sure exactly what their relationship with Fujitsu was, possibly Fujitsu may have kept the underlying IP and UTS Global just sub-licensed it.) It appears UTS Global has gone out of business some years back. I think their main customer were certain US telephone companies using certain legacy apps maintained by Telcordia; I think once those companies migrated off those apps their business was gone and they just disappeared.
Fujitsu's mainframe business is still going. Their Japanese mainframe business (which pre-existed the Amdahl purchase) is still alive (although I don't think it is sold outside Japan any more, back in the 80s thru 90s Fujitsu's FACOM mainframes were common in Australia but I'd be surprised if any remain here). In Europe, they own non-IBM-compatible[1] mainframe lines – they bought ICL whose mainframes are still used by UK government, and they bought Siemens' BS2000 mainframe business which is still used in some European countries (especially Germany).
No idea what Fujitsu's attitude to hobbyist use is. I've never heard anything positive about it. (On the other hand, unlike IBM, I've never heard anything negative about it either.)
[1] To be strictly correct, BS2000 is partially IBM compatible – the original instruction set is based on S/360 but not 100% compatible with it; that original instruction set ended up being emulated on SPARC and later x86; the OS is very different from any IBM operating system.
As I recall, the original UTS ran on top of VM/370, but the later, native version relied on being on Amdahl hardware. I don't recall what specifically was required.
And, yes, IBM would likely frown on passing out copies of AIX.
That'd be cool.