No, but if this team finishes with a bad enough record then they don't really have a choice, now do they? If you are bottom 3-5 bad with one of the oldest teams in the league (that isn't getting any younger next season), then there isn't much Rogers can do to force a run at the playoffs.
That is why it is imperative that this team doesn't go on some pointless run to hang around aimlessly while still missing the playoffs by 5+ games. In that situation it is entirely plausible that Rogers demands making a few moves and having another go next season, which will end with the exact same result because this simply isn't a playoff team anymore the way it is constructed.
The point that you are missing is that this team is crap already and they haven't traded a single player yet. IE: the losses are coming and the seats will be empty regardless. There is no saving this buddy; the team is reliant on far too many really old players who aren't getting any better, and will in fact get even worse. What is your saving solution? You'll go into free agency next year and somehow patch all the holes and pray to god that Martin/Tulowitzki/etc/etc all have career years? Oh, while also likely replacing Estrada and Liriano? Its not happening.
Shapiro and Atkins were specifically brought in to dismantle this team back in the summer of 2015. Remember, when he was hired, this was a middling old team, that got older when AA cleaned out the farm system to make its run. Guess what, it worked for the next 2 1/2 months, and ownership got a taste of the success on and off the field. So they didn't dare blow this thing up. They couldn't after Bautista hits that bomb against the Rangers. At the same time, that winter, they do nothing to improve and add to the core. The only thing, they did, was shuffle the deck chairs. Never stepped up once that winter to ADD TO THE CORE, just tried to keep the status quo. Low and behold, they again are a playoff team. So out of necessity, because of the continued success off and on the field, they increase the payroll for this year by approximately $30M, TO TRY AND STAY COMPETITIVE (Remember Shapiro scolded AA shortly after being hired, for cleaning out the farm). Just imagine, if they had increased the payroll after the 2015 season, like they did this past off season? The success, that this team has had, must be causing Shapiro fits, as he was brought in to clean up the mess. The WINDFALL PROFITS, that this has generated, has lead to everyone calling an audible, and they want to continue to count and fold "Dead Prime Ministers."