Going into the offseason with a winning streak is definitely something positive, but how much would that outweigh the losing record and worse draft pick?
I want to see the Bears win, but also want them to have the best draft position as possible. Even if they don't actual pick someone, dropping from #11 to #17, is the equivalent of losing a late 2nd round pick. Having the better draft pick also gives them more options. Pick, trade down, trade up for less, etc.
Also, the Bears have had the 2nd hardest SoS this season, so they would draft last after all the team's of the same record, with the exception of Philly.
Either way, playing NO in Chicago gives the Bears a favorable matchup. My best scenario would be a Bears win and still get a mid teens pick (13-15).