No because serving the suspension would be admitting guilt. If it were me, I would fight until the very end, especially if I felt I was innocent. This has a direct effect on Brady's legacy as one of the GOAT. He absolutely should stretch it out as far as he can.
It will be very interesting to see if the NFL allows the third party investigator to be used. If they do and Brady is found to be guilty, then I will support the penalties 100%. If they DONT allow the investigator, that will be very telling.
Just because the NFL has upheld suspensions for such things doesn't make it right. The way the NFL has handled the Hardy, Rice and Peterson cases have turned them into complete jokes.
They stole the Lance Armstrong playbook. Problem is, the truth tends to come out, and when it does, it makes you look even worse than if you had simply admitted it in the first place.