As long as the appeals process is ongoing, any penalty that Mizzou is appealing is on stay - which means temporarily lifted until there's a final decision.
If Mizzou appeals the postseason bans, which it surely will, and the appeals committee hasn't made a ruling by the end of the football season, the team would be eligible to play in a conference championship game and bowl game.
Now, that's 10 months away. The appeals process begins quickly. Will it last 10 months? That seems like a stretch to some degree, but you never know with the NCAA.
The Committee on Infractions made its initial ruling on Ole Miss on Nov. 1, 2017 ... and the appeals committee issued its final decision on Nov. 1, 2018. A full calendar year.
Notre Dame's COI ruling came out in November 2016 ... and the appeals ruling came out in February 2018.
So, the process can drag on for up to a year or more. There's just no telling how long it will take.