A new, more flexible mechanism for enforcing the 100K limit on the number of SNS neurons has recently been proposed and adopted.
With https://dashboard.internetcomputer.org/proposal/132151 being adopted, new swap participants will now be rejected if the maximum number of SNS neurons required for earlier participants (100K) has been reached. Users who cannot participate in the swap due to this limit would observe an error popup with an explanation (displayed as a popup in the NNS dapp). All the ICP that did not end up participating in a swap is of course refundable, as before.
In this scenario, the early participants would still be able to increase their participation, helping the swap succeed.
With https://dashboard.internetcomputer.org/proposal/132377, the strict constraint described at the top of this thread is no longer enforced at SNS initialization time. While preparing for a launch, one should thus ensure that the minimal participation amounts are not too small, as that would make it cheaper to flood an ongoing swap with a large number of small participations, potentially limiting other community members from being able to participate.