I'm not positive about Penn State, but I do think you have a shot at a better school.
But you'll never know unless you apply! My suggestion is to apply to one or two "dream schools" like Penn State.
If you have time to take and do well on the SATs, I would do it. If not, don't bother.
I don't know if this is how colleges see it, but I personally think it shows a lot of commitment and personal dedication that you got your GED. So if only from me...congrats on that