The simple answer is no. DWR is a surface treatment and does not impact the performance of the waterproof membrane.
Both properties are separate, meaning when the DWR wears off, a waterproof jacket is still waterproof. Waterproof ratings are determined without considering DWR. A well-maintained DWR treatment will, however, help your jacket breathe very efficiently by minimizing saturated outer fabric and maximize your comfort.
No matter your product, the story is relatively the same. It’s important to monitor and maintain your jacket for optimal performance.