I would not use a dry vacuum on a damp carpet. My day job is as the owner of a Janitorial Supply Distributor. I fix vacuums all the time that have rusted motors casued by someone vacuuming the carpets when they are wet. You will get away with it for a while but it is not long term. If you deal with damp carpets, where damp is defined as a vacuum will take out moisture I would suggest investing in a spotter which is nothing more than a mini extractor. You could also let them air dry or force dry them with a air mover type fan.
I have a spotter, a steamer and a wet dry vac. I extract my interior 1x per year after the winter and when the temperature is above 40 degrees. I dry vacuum, pre spray, extract with just water and then extract with just vacuum.
You can also get quite a shock vacuuming wet carpets with a dry vacuum!