No, Linux takes binary compatibility seriously. I can run statically linked binaries from 1992 on a modern system just fine.
ELF was being slowly introduced in 1994, with Slackware 2.0 being one of the first distributions to support it.
http://www.linuxjournal.com/article/1059
So I really really doubt you can pick a static executable compiled against kernel 0.x.y, using a.out format and execute it in Ubuntu 16.04 LTS as example.
Actually, I just need to take the dust out of my Walnut Creek CD's to prove my point.
Not to mention how disparate the file system structure, including device drivers, of something like Yggdrasil Linux 1.0 is compared with modern distributions.
As I said, easily verified by dusting off Walnut Creek CD's and picking a random binary from them.
If dynamic linking was used, the entry points might have been moved, the syscalls have changed, bugs are were being taken advantage of were fixed.
If static linking, the calls into the kernel might have changed or data read from /etc, /dev or other type of expectations from target OS.