Yes, the fact that Lily Pulitzer held a big sale with a hard deadline to purchase the items shows that this bit of psychology helps to push the brain. When stress is a huge factor of a job or duty to be carried out, most people seem to revert to 'fight or flight' courses of action. Some people will fight, like Lily Pulitzer and be greatly successful in a stressful situation, and others will choose the flight method and stop or give up.
One of the most basic marketing strategies is to make customers feel like they can ONLY get this deal if they act RIGHT AWAY. This sense of urgency makes the item much more important in the mind of the customer. Lily Pulitzer knows this as well as anybody, and when it's all over I expect the brand to do very well with this approach.
When companies push a big sale for a limited time, it does help push the brand. Consumers won't want to miss their chance at big savings, so they will rush to buy products, even if the entire 'sale' is only an illusion. The Lily Pulitzer sal helped push the brand by increasing sales.
This just seems pushy. Of course devoted brand followers will follow suit and buy, but others will be turned off. Anyone who demands a purchase-by-date (an item that doesn't expire) should be put out of business by the consumers in the market. There are so many brands willing to bend over backwards to get purchases, and that is more welcoming than Pulitzer's style.