Can Uber take you out of the coverage area?

Yes, they can.

By coverage area, I assume you are referring to the area in your city where Uber picks you up. 

Yes, you can take an Uber ride to locations outside of this coverage area.  While the drivers are only allowed to pick up passengers in their home location (where they are registered), they are allowed to drop off in others. (See: Driving in other cities)

With that said, you want to keep in mind a few things:

• Ask your driver: After you've been matched with a driver, you may want to contact the driver and ask if such a trip is ok.  Sometimes, drivers would prefer not to travel that far or they may be close to the end of their shift. It is a courteous thing to give them a choice.
• Duration Max: The catch is that there is actually a duration limit as to how long a ride can be. At some point, Uber app will automatically complete the ride. At that point, you can request another Uber, granted they have service there. (Source: Is there a maximum distance the driver will bring you?)

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Uber Driver, CEO of TaxiFareFinder and Unleashed, LLC