There's not a real specific timeframe, for example, but I expect it's unlikely. Redistricting is a complicated process, and usually ends up in the courts regardless. For example, Virginia's last redistricting plan is still being looked at; SCOTUS sent it back to the lower court earlier this year. Meanwhile, Wisconsin's most recent plan is currently under consideration by the Supreme Court, with oral argument happening about a month ago. In that case, it wasn't until 2011 that Wisconsin even put its plan out there, and then it wasn't ruled on by the first-level court until 2016.

(For more on this case, SCOTUSblog's In Plain English summary is good, and this law review article on the history of gerrymandering is worth a look too.)

Nonetheless, having a majority in 2020 would at least allow the Democrats to get the ball rolling. What they can do will depend in large part on how the Supreme Court decides the Wisconsin case, since the last time this was heard (in 2004), the Court punted by saying that courts couldn't rule on the question of partisan gerrymandering at all, since no one had been able to figure out a good way for that to work.