There's no reason why they can't, because the flames are from unburnt fuel escaping past the exhaust valves into the pipes. Fuel pooling around the inlet valve has nothing to do with it.
However, the idea behind direct injection is to try and ensure that all the fuel injected into the cylinder is burnt by more accurate timing and location of the injected fuel. If DI road cars are going about dumping unburnt fuel and shooting flames, it sort of defeats the point (race cars shooting flames are due to their fuel and ignition mapping being pushed hard, and isn't really applicable to road cars).
Faster, faster, faster, until the thrill of speed overcomes the fear of death...
– Hunter Thompson