This weekend, when I went to Castles N' Coasters, I decided to try this out for myself. My natural inclination would be that yes, P3 and P4 should be angled to the screen in order for things to feel right. They have a few 4 player games there, and I checked - all the joysticks from the factory are installed straight up (no angling).
I put some credits in and I used the P3 controls (far left). I started off by playing straight-forward, directly in front of the machine. Obviously, I had no issues. I then, stepped to the side, playing as if I were the third player and someone were occupying the P1 area. Although my body was angled towards the screen, I had NO issues with the joystick. When I wanted to move up on screen, reflexively I pushed the joystick in the up direction relative to the screen, not "up" relative to me. It the same with the sides. I even moved so that I was standing on the side of the cabinet altogether (you should have seen the looks I got), but it made no difference. You just instinctively know where to go.
So there you go, tested out in an arcade on a real machine 5 days ago. You don't need to angle your sticks.