Am I correct that cyclical unemployment can be negative?
Cyclical unemployment $U^C$ is by definition difference between actual observed rate of employment $U$ and the natural rate of employment $U^N$ so we have: $U^C_t \equiv U_t-U_t^N$, see for example this paper.

Hence cyclical unemployment can be negative if actual observed rate of unemployment is lower than natural rate, because it is defined as a difference between the two.