Clockless computers don't have a global clock but they still have components that "tick".

Depending on the design, no more than abacus has components that "tick". And I'd never say an abacus requires a clock to function.

If even a single bit gets hung up in a straightforward clockless design, everything else waits for it.

None of that is really visible to something inside the computer, though. The OP is describing calculation steps, not clock cycles.