Let us assume that you "initate" maximum braking at or before V1, but you detect that you are "achieving" no braking and you exceed V1. Do you really "continue to reject"?
Seems like you're wasting a worry
Lead Balloon. As was said, you'll be on your own, and the very first to have experienced NO brakes. The following was not a brake failure per se (as in no brakes), but an inability to absorb the degree of heat generated.
The investigation of one recent RTO incident which was initiated “very near V1”, revealed that the overrun was the result of 8 of the 10 wheel brakes failing during the RTO. The failed brakes were later identified to have been at advanced states of wear which, while within accepted limits, did not have the capacity for a high energy RTO.
This was the first and only known accident in the history of commercial jet transport operation that can be traced to failure of the brakes during an attempted RTO.
https://www.faa.gov/other_visit/avia...off_safety.pdf