Fermenting under pressure won't completely carbonate a batch. At most, it will partially carbonate the beer. You still need to complete the carbonation process.
I'm fermenting in conical fermenters at this point, where I can ferment under pressure (rated working pressure is up to 15psi) and then attach the carbonating stone setup and finish it after I chill the beer to carbonating temperature (glycol chiller). I do this even with batches where the fermentation pressure level is close to what I'll use to carbonate it. Mostly because there's a pressure drop with the temperature drop.
I set the pressure of the fermenter depending on the yeast I'm using and if I want esters or not. If I do, I set the pressure lower (5psi max). If I don't, then I set it in the 10-12psi range. For this reason look at information for the yeast you're using to see about ester production. Some recipes do well with it, where others not so much. Don't just blindly think that more pressure is better, trying to get it fully carbonated without doing anything else.