I imagine other parameters are more important (like temperature or pitching rate). Still, I was wondering if pressure has some effect on the fermentation process (for example on flocculation, fermentation time or flavour profile)
I found a study on the effects of brewing under pressure. The general conclusion was that increased pressure reduced the formation of esters and fusel alcohol. This was caused at least in part by a reduction in the amount of yeast growth as the pressure went up. Judging by the active vs total biomass charts, it did not have any noticeable effect on flocculation.
Pressure matters. Most commercial breweries deal with significant hydrostatic pressure as a result of their large conical fermentors, though this effect is negligible at the homebrew scale. Still, many people (myself included) ferment under pressure.
The dominant effect seems to be a slight reduction of esters, and as I understand it this is linked to decreased production of Acetyl CoA. But, to increase esters again, I simply ferment a few degrees warmer than I otherwise would. It's a relatively subtle variable, but important nonetheless.