Understanding the physical processes driving deep convective storms is an essential prerequisite for understanding the wider tropical atmosphere. Cold pools driven by rainfall evaporation are a ubiquitous feature of Mesoscale Convective Systems (MCSs) that have especially pronounced upscale effects in the climate of the West African Sahel, through their modulation of the regional monsoon circulation. The role of cold pools in determining the dynamics, lifecycle and propagation of tropical MCSs themselves, however, remains debated. Here we probe the feedback of cold pools on Sahelian MCS characteristics through a 40 day, 2.2 km convection-permitting Met Office Unified Model sensitivity experiment in which rainfall evaporation is switched off in the microphysics scheme. Storms generated in the sensitivity experiment subsequently show strongly suppressed cold pool density currents versus a Control simulation. Yet we find no statistically significant difference between the diurnal cycles of MCS counts, with continued nocturnal propagation of storms in the experiment, and a reduction of MCS speeds by 1.7 ms^-1 caused by a similar slow-down in the African Easterly Jet due to changes to the large-scale meridional temperature gradient. Changes to composite updraft geometry are consistent with the role of cold pool horizontal vorticity in balancing the strong low-level wind shear characteristic of the region. Remarkably though, we find no sensitivity of the positive scaling of MCS rainfall with shear to cold pools, with reduced entrainment-dilution under stronger shear conditions remaining the fundamental physics driving the relationship. Our results help to disentangle processes in the Sahel in which cold pools play a driving role (nocturnal rainfall intensification, regional circulation) from those in which they are passive actors, which we find primarily to be MCS development, propagation, and rainfall-shear scalings.