I think to get the real answer we would have to ask the mint, but from my experiences this is what I believe happens.
1) There is an automated checking process. Once an order is placed and a hold put on a Credit Card, the units available get reduced by that amount.
2) The orders go into a processing step.
3) Once the processing units equal a predefined number (lets say 175K for the
Peace dollar) the item is marked no longer available and all sales stop.
4) After the processing step the orders are confirmed. Basically, did you buy the allotted amount, is your address and CC information valid. This is probably automated also.
5) If you meet all checks the order gets processed and in the case of the
Peace dollar goes into Back-Order and gets added to a queue to be filled once the item is available.
6) For orders that fail the automated process they get added to a queue for manual review (one of my orders went into this as it was my 4th order and should have free shipping).
7) Due to the number of orders this can take from a day to a few days to a week or longer. My 4th order stayed in processing for 6 days.
8) At the manual review time the US Mint has the final say as to what they are going to do. If you ordered 4 and the HH limit was 3 they (the mint) might reduce the number or cancel the order.
The mint on their website is very vague on how they will resolve this:
"If an order has outstanding issues (such as credit card holds, household order limit violations, or address verification conflicts), the next orders in line can be fulfilled before the one with outstanding issues. While the issues for an order are being worked out, the status of an order may display "hold" during this time. Once the outstanding issues are resolved, the order is re-inserted next in line. Accordingly, such re-inserted orders will not be processed for shipment in the same sequence as their order numbers."