Does the drying out of vegetables affect the taste after cooking?
8 hours in still air is probably not going to be enough to thoroughly dry your vegetables.
If you live in a very dry climate and the veggies were sitting uncovered in front of a fan the entire time then you might have actually dried them.

So your title is asking a different question than your description.

Description: 
If you live in a very humid climate then you might be more concerned about spoiling than drying. They may have become a little limp so it makes a difference how you plan to cook them. If the veggies are going to be diced and sauteed and used in something else then they will probably be fine. If they are going to be their own side- like steamed asparagus- then the texture may be decidedly un-fresh.

Either way- the flavor will be normal or close to it.

Title:
Actual dehydrated veggies are different altogether. They have had most of their water removed. This concentrates flavors and changes them. They are sweeter and more intense. Their texture is also firmer and ranges from crisp to rubbery to almost normal depending on how much they are rehydrated.