So, we understand that the carpet and pad are unlikely to dry quickly enough by themselves. However even if they did, is that you have to issue yourself with when your carpets are damp? No, it's not.
Whenever possible use fans and air conditioning unit to distribute the air much faster and help speed up the drying process. After about ten to twelve hours the carpeting need to prepare to lay flat again. As soon as you lay it flat keep the air circulating and if you have a dehumidifier turn it on.
Your water damage restoration specialist should likewise let you understand if you have any water-damaged (wet) structure in your crawlspace and establish a drying strategy and estimate