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.
Chances are pretty good that the W&B was recalculated automatically as soon they decided to let you board. Pax manifests have to be accurate and just about everyone uses software tools to manage this. Once you have a pax & bag count, you plug the numbers into whatever zone they're in and boom done.
It depends. If the pilots had already completed the loadsheet, or received it from the handling company (more likely for a larger operator), then yes, they do have to recalculate, or request a new, updated loadsheet.
Otherwise, since no loadsheet has been issued, there is nothing to recalculate, for the pilots, but WHEN the loadsheet is calculated, it WILL include the latest numbers. Bottom line is: you will be included.
400 kg is enough to make a noticeable impact on performance (engine thrust setting) and take off speeds for a 737.
As another poster implies, there is often a last minute change (LMC) section for, well LMC's. There is also an upper limit of how large this LMC can be (ranging from 500-1500kgs for the 737-operators I have been with). An LMC usually takes about a minute.