This is just my opinion... And it's not worth much...
But from reading bits and pieces from the Wells report and the charges handed down to Brady...
I can't see a reduction in the penalty... And I can definitely see him appeal...
But I'm thinking he will either win and not get any weeks... Or lose and cop the 4 weeks.
I say that because from what I've read he's essentially been punished for not cooperating with the investigation.
The Wells report itself suggested he had known, but it wasn't definitive. Not enough for a 4 week suspension anyway... I think the NFL have said that there was enough smoke to suggest if Brady DID provide all the requested evidence they would have been able to make it definitive.
I think for Brady's team... They will argue that it's not up to Brady to provide details which can incriminate himself... And that the burden of proof sits with the league in this instance. And with the Wells report being ambiguous at best as far as Brady's involvement is concerned, if they can convince a judge that he cooperated to a satisfactory enough level they could get it overturned IMO...