Yes, the boot screen displays at 480i. Some games run at 480i. Some games have menus that are in 480i, but the game itself is 240p. Most are just 240p, though.
I just had a weird thing with SpongeBob SquarePants: Revenge of the Flying Dutchman for the PS2. The game runs at 480i but when a loading screen with a small still image appears, the PS2 outputs at 240p for that screen but once it goes away, the PS2 goes back to outputting 480i. I've heard of loading screens and title screens running at 480i and the rest of the game running at 240p but not the other way around. Why does it do that for a simple loading screen?