November 27th: One-Year Residence

Since Balk is permitted to compete in January with the waiver and assuming he meets all NCAA PTD requirements, can he compete for OSU starting in the spring 2019 semester?

No.  NCAA Bylaw 14.5.5.5 states that in baseball and basketball, a student-athlete who initially enrolls at the certifying institution as a full-time student after the conclusion of the first term of the academic year and qualifies for an exception to the one-year residence requirement shall not be eligible for competition until the ensuing academic year.
(See Bylaw 14.6.1.1 for the application to graduate transfer student-athletes.) (Adopted: 6/24/09, Revised: 4/26/17 effective 8/1/17)

Would the answer be different if Pop graduated from James River Institute in December and transferred to OSU as a graduate student?

Yes.  NCAA Bylaw 14.6.1.1 states that in baseball and basketball, a graduate transfer student-athlete who initially enrolls at the certifying institution as a full-time student after the conclusion of the first term of the academic year and qualifies for the one-time transfer exception may be immediately eligible for competition, provided he or she satisfies all other applicable eligibility requirements. (Adopted: 4/26/17 effective 8/1/17)