Megan,
Please go and look up the proper certification definitions, please, not popular shibboleths. It is really quite important in the understanding of what V1 actually is, as opposed to popular misconceptions.
Please use authoritative documents, not common "text books", FCOMs etc.
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"?
That is when you are really on your own, but by that time the thrust levers will long since be at idle ( or should be) ----- there are a number of instance over the years of something like this, not necessarily an engine failure, sorry, but I don't have references, but the outcome was never a happy one.
Tootle pip!!.