Presumably the rocket engines in the center of an engine cluster would be surrounded by lower-pressure exhaust from the outer engines so essentially the "atmospheric pressure" around the center engine would be lower, resulting in a higher specific impulse. Is this correct, and has this phenomenon been observed?
tl;dr If anything, the flow field interactions hurt the performance of the center engine(s).
The calculation of the flow field for a multiple rocket engine cluster is extremely complicated and the effects on the base force (see What does the Shuttle's axial forces analysis reveal? and What is the plume effect? for info on the base force) are likely, when integrating all the forces over the vehicle, to swamp any changes in engine thrust. Here's a simplified flow field example
The negative effect on center engine thrust due to an effective increase in ambient pressure is explained in the same paper (emphasis mine)
Three-dimensional simulations are carried out for the underexpanded jets with a NPR of 7.2, where NPR is defined as the ratio of nozzle exit and ambient static pressure
The pressure values after the external shock are higher than the ambient pressure and hence the effective NPR as experienced by the jets is smaller than the NPR of 7.2.
A reduced NPR equates to an increased ambient pressure and therefore a drop in the pressure thrust term (see From the General Thrust Equation towards Tsiolkovsky, how to explain dropping these terms along the way?) The momentum thrust would be unchanged, thus a net loss in thrust results.