I don't think its entirely a no brainer. Ted Olson is one of the top appellate guys in the US, so he is costing serious money. Serious money against a long shot appeal.
The only edge here is that if they get granted a review, then the 3 man Court of Appeals opinion is stayed and Brady plays this year. It would be nearly unheard of for this to be heard before the season.
I wish there was a way to try Roger and the NFLPA leadership on a kangaroo court and sent the all to an Italian Basketball League for 5 years.