With Tom Brady getting shutout against the Saints, his MVP hopes are probably hurt some, which gives Rodgers the momentum in the MVP race, but not since 1999 has the player that won the MVP, also won the Superbowl.
From wikipedia
In recent years, if a player that won the MVP makes it to the Super Bowl, the MVP often loses the Super Bowl in the year they won the MVP. That includes Brett Favre in 1997, Kurt Warner in 2001, Rich Gannon in 2002, Shaun Alexander in 2005, Tom Brady in 2007 and 2017, Peyton Manning in 2009 and 2013, Cam Newton in 2015, Matt Ryan in 2016 and Tom Brady in 2017.
So since 2000, MVPs don't win the Superbowl the same year they win MVP.
Though looking though these, another recent pattern has happened.
2017 season Tom Brady wins MVP and then for the 2018 season wins the Superbowl
2018 season Tom Brady wins MVP and then for the 2019 season wins the Superbowl
2019 doesn't work, as Lamar Jackson won the MVP and in Tom Brady won the Superbowl...
But in 2020 season Aaron Rodgers wins MVP and then for the 2021...
Based on patterns (which mean absolutely nothing) Rodgers has a great shot of going to the Superbowl in 2021. Though winning nthe MVP this year might not be helpful for actually winning the Superbowl at least if you believe in superstitions. (And I'm not saying you should, but patterns are interesting still).