Do the pilots have to recalculate the balance when 6 passengers show up last minute in a 737?
Loadsheets have a section called 'last minute changes'. As the name implies, pilots can record last minute changes here. If the changes are minimal, there is no need to recalculate the mass and balance, and trim settings. 

What constitutes 'minimal' depends on many things, principally limits set by the operator or manufacturer. I can't verify this but think 400kg would fall within these limits, unless the aircraft was already at its performance limits.