Semi slicks, or slicks will possibly make you experience an oil surge. I know Toyota NZ has developed a baffled sump for the TR86 race cars to help prevent the issue.
The TR86 car's all run oil coolers and full slick tyres and with the addition of the baffled sump don't appear to have any problems on any of the tracks tested here in NZ.
Unfortunately they don't want to sell the baffle plates to the general public just yet
BTW, I don't think an oil cooler would do anything to change the issue with the oil surge, because when you install the oil cooler, you add more oil to fill it up. The oil passing through the cooler is the oil already picked up by the pump so doesn't affect oil starvation at all. My theory being is that the oil cooler has no air in it, so even under high G cornering, oil going into the cooler = oil coming out. If you had air in there, then the air could be displaced with oil under a hard corner, but I think your sump would give you issues before the oil cooler would. (Could be wrong on that, but I am sure someone will correct me if I am)