The tax return is considered "filed" when it is postmarked, not when it is received. While I can't find any information on New Jersey, specifically, I imagine they follow the same rules as the IRS which allows a few days for taxpayers to get a mailed return postmarked after an e-file rejection before it is counted as "late".
However, you're correct - filing the extension buys some protection and is a good idea to cover your bases.
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