Can A 1-Bit Computer have more than 2 Registers?
Many 8-bit CPU architectures have instructions that consist of more than one byte. I see no reason why a 1-bit CPU could not similarly have some instructions that consist of multiple bits.

At a more general level: The "bit-ness" of a CPU typically only reflects the size of its registers. It's perfectly possible (and, indeed, quite common) for instructions, the address bus, and/or even the data bus to be different widths from registers.