No, you cannot use your UC-200 with private well water. The UC-200 is designed exclusively for municipally treated cold water.
It is not rated for well water or any water that is microbiologically unsafe. Using it with well water will void the warranty and will not provide the necessary protection.
If you have well water, you require a different filtration system. You should contact APEC Water for systems designed to handle different contaminants, such as a reverse osmosis system. Their phone number is (800) 880-4808.
Remember, the unit must only be connected to a cold water line. Never hook it up to a hot water supply.