can the pitcher run to first base with the ball and get an out?
Yes. It doesn't matter how the ball gets to the base, if a player touches the base with control of the ball before the runner gets there, the runner is out. The pitcher could throw, kick, or roll the ball to first if they wanted to. On rare occasions, the ball will get stuck in their glove so a pitcher will throw their entire glove (with the ball inside) over to first base!