1945-S Lincoln Cent - Multiple Errors - Should It Be Graded?

The obverse struck-thru error might have an impression of the central axis of the wheat ear on the opposite face. If so, your coin would have brockages from two struck fragments. Since each brockage is aligned with the normal raised design on the opposite face, this would indicate that both fragments entered the striking chamber unaccompanied by a normal planchet, were struck, clung to the obverse and reverse dies, respectively, and were struck into the next planchet (your coin).