Once they're chilled to drinking temps you can go ahead and drink em. Extended time in the fridge will help clear the beer and compact the yeast. The "finish up the process" idea comes from the fact that if you open a beer before it has been properly chilled i.e. too warm, you will get a pfft when you crack the top, but possibly flatter beer than if you had allowed the beer to fully chill. This is because more gas (CO2 in our case) can dissolve in a cold liquid (beer) than in a warm liquid.
Primary - Mild, Bitter, PB Stout, IIPA, Apfelwein, American Brown
Bottled - I Drink Because I'm Gourd, Jurassic Park Amber, Short and Stout, Barley Motivated, Romney Pale, The Seven Dwarfs IPAs, Roggen' Robin, Double Table APA, North o' Britain Brown, Apfelwein