Is assembler portable between Linux distros?

You might want to check out LLVM before going down this particular path. It might make your life a lot easier, as it provides a low level virtual machine that makes a lot of hard stuff just work and has been very popular.

At a very high level, the ABI consists of { instruction set, system calls, binary format, libraries }.

Distribution as .s may free you from the binary format. This is still rather pointless, because you are fixed to a particular ISA and still need to use libraries and/or make system calls. Libraries vary from distribution to distribution (although this isn't really that bad, especially if you just use libc) and syscalls vary from OS to OS.

It's basically 20 years since I last bootstrapped a C compiler. At the level of compilers, the differences between Linux distributions are minimal.

The much more important reason for going LLVM is cross-platform; if you're not writing some intermediate language, your compiler will be extremely difficult to retarget for different processors. And seeing as, on my laptop, I have compilers for x86, x86_64, two kinds of MIPS, PowerPC, ARM and AVR... you see where I'm going? I can compile multiple languages for most of those targets too (only C for AVR).