Short answer
Complexity only increases delays when neurons are serially linked together.
Background
Neuronal conductance of action potentials takes time, as neuronal signals travel at a speed of 0.5 to 150 m/s through the axon (Purves et al., 2001). Furthermore, synaptic transmission between neurons takes time (in the order of 0.5 ms (Katz & Miledi, 1965) As a consequence, stringing neurons together increases processing time.
For example, if we look at the pain response, the reflex arc is very short, covering as little as two synapses (Fig. 1). The moment you touch a hot pan, you pretty much instantly draw away your hand. This process precedes even before you become consciously aware of the fact you touched something painful. This is because conscious awareness happens in the brain, involving a longer distance to be covered from your finger, and because it involves many more synapses including the brainstem, lower cortical areas and higher cortical areas (Fig. 2).
Fig. 1. Pain reflex. source: Owlcation
Fig. 2. Conscious pain pathway. source: neuwritewest
References
- Katz & Miledi, J Physiol (1965); 181(3): 656–70
- Purves et al. (eds), Neuroscience, 2nd ed. Sunderland (MA): Sinauer Associates. Increased Conduction Velocity as a Result of Myelination