Do the pilots have to recalculate the balance when 6 passengers show up last minute in a 737? Few years ago me and my mates forgot the checkin time and were late for flight. We were late for check-in counter closure (30 minutes before flight if i'm not wrong) but the staff allowed us to go on. We had no checked luggage. There were 6 of us so at least 400 additional kilograms to be carried. Do the pilot need to recalculate mass and balance or is it within the allowance?
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.