Not really. If the contractor is very careful and you are really lucky he might be able to pull them out and then reinstall them after the new cabinets are installed. A lot of this will have to do with how well the counters were installed in the first place. Also, the existing countertops may not line up with the new cabinets exactly in some areas as well as they do now. The better option is to have the cabinets refaced, leaving the boxes and tops in place. Unlless you have deteriorating particle board cabinets you should be able to get a carpenter to do this. If you decide to remove the countertops and install new cabinets factor in new tops and be pleasantly surprised if they can be reinstalled afterall. Realize you probably won't find a contractor willing to gurantee not damaging the tops. If you do, dig in and research him well. He likely doesn't have enough experience.
Todd's Home Services
San Antonio, TX
As long as the counter is big enough Corian is one of the easier ones to work with. Since it does not have the ground or crushed stone that some of the other material have you can work with normal woodworking tools. A saw with a fine tooth carbide blade and a professional grade router with the proper shaped carbde bit can be used if the edge needs finishing. A belt sander helps on cuts also. The only problem you might have is if you need the joint kits for seaming as I dont think you can buy them.
When Corian first came out I could buy the slabs and fabricate my own tops and then Dupont went to a certified distributor system and would no longer sell to those of us that had been working with it for years. I will admit that they did have reasons for this as not all that were working with the product were doing it right.