Are my new stone countertops going to be level?

The answer depends entirely on who is completing the work and the quality of cabinet installation. Many people who are getting new Silestone or granite countertops will assume that they will be installed straight and level and that all installers are basically the same. They are quite disappointed later when they find that their seams are wide and stair-stepped and eggs and oranges roll off their uneven countertop. Ask you installation company what their seam width and rise tolerances are. You may be surprised at what you hear. The "hurry-up" low-priced installer's response to the customer is usually always the same..."that's the best we could do with what we had." Not true. It's only the best they could do because they either weren't experienced enough to do better or simply wouldn't take the extra time.
It is completely possible to get a table-top level installation and nice looking seams for almost all kitchens if all parties involved do their jobs. And when it is not possible, the consumer should be notified and shown the defects in their cabinetry that will cause problems. We insure that the proper steps are taken by both cabinet maker and countertop installer to get the correct end result. We use a propietary checklist designed specifically by us over the years to help the consumer through the process. We also personally do all our templating and installations.
If you are installing stone over existing cabinets and there is no cabinet maker, then your cabinets are probably NOT level. Why? Because you most likely have laminate and its bendable. It easily hides cabinets that are not level. This is where the experienced installer can make the difference in the final product. He will need to spend extra time shimming and caulking to achieve the best possible outcome.
Tabletop level countertops are rarely the norm these days and there are many installers who won't shim very much, if at all, so take matters into your own hands and insist on superior quality of workmanship and project accountability.