This might be why the code space alphabet is defined by the standard so it will at least put an emphasis on 8 bits == 1 byte.
The question, though, was about whether it's the minimum addressable unit of memory. In the C memory model, it is, but by implication - you can't have two pointers that compare non-equal, but differ by less than 1, so a type with sizeof==1 is by definition the smallest you can uniquely address. However, the C memory model doesn't have to reflect the underlying hardware architecture.
The CPU itself used 32-bit addresses to access machine words, the size of which was determined by what was being accessed. External memory was limited to 32-bit. Internal memory had regions that could be 32-bit, 40-bit, or 48-bit. An address increment of 1 would thus move by that many bits.
Mercury Computer Systems shipped a byte-oriented port of gcc. Pointers to char and short were rotated and XORed as needed to reduce incompatibility. Pointers to larger objects were in the hardware format. This allowed a high degree of compatibility with ordinary software while still running efficiently when working with the larger objects. There was also a 64-bit double, unlike the 32-bit one in the other compiler. Data structures were all compatible with PowerPC and i860, allowing heterogeneous shared memory multiprocessor systems.