Were there 2 separate registration codes, or just one?
If there was only 1 code, then regardless of what content you can download, your PS4 access is likely registered under your Mogstation account as access to ARR and Heavensward as a single item instead of two seperate entities. This would prevent you from logging in on the PS4 until the proper date for HW.
If there was 2, well, back to being uncertain I guess.
edit: Wait, this bundle doesn't release until Heavensward does. Regardless of the fact that ARR is a part of the bundle, it's still subject to the bundle's release date.
edit 2: Also, the ARR/HW bundle does not carry the early access pre-order bonus, so you won't have access to FFXIV on your PS4 at all until HW's official launch date.