This is for the case of a hydrogen fuel cell. My reasoning was that, similar to rates of reactions, increasing gas pressure increases the 'concentration' of the molecules, thus there's more reactions. I guess that that would more likely affect the current though.
Pressure has significant influence on the cell voltage only if some active components of redox systems are gaseous.
Otherwise, the effect is very small, depending on slight volume and/or compressibility changes. These can be both ways and higher pressure would support the state with smaller volume, with (near) negligible effect.
There cannot be therefore said in general if higher pressure would increase or decrease the cell voltage.
In later added context of hydrogen fuel cells, the cell voltage would increase with pressure of hydrogen and oxygen gases for two reason:
- Thermodynamically, electrode potential of the oxygen electrode would increase due increased activity of oxidant(oxygen). And vice versa for hydrogen as reductant. Both effects would increase the open voltage of the hydrogen fuel cell.
- Kinetically, increased pressures would increase rates of redox reactions, decreasing the cell voltage drop under the load, so it would for the given load provide the dynamic part of voltage increase.
There will be also possible minor effects caused by pressure affecting geometry of the cell design.