No, it would need to be autorun, otherwise the player could just walk away.
Why do you have a whole event page with a condition JUST to turn on a self switch? Take the commands from page 2, and put them on page 1. Then make it autorun.
The event will also only move one step towards the player (because that's what you told it to do), and if there's something blocking its path, it won't move at all.
However, NONE of those event pages would actually run, because you've got them set to Action Button. It sounds like you've either done something to the tiles on the map so that you can't move, and it has nothing at all to do with the event (check that the top left tile in the Tile B tab has a star on it and not an X), or you've got some other event that becomes active when you go to this map, that's set to Autorun, and is never being turned off. An autorun event, even if it has no commands, will stop the player from moving.