Yes.
If there are more people requesting rides than drivers available to give them, fares will increase via surge pricing. This will be reflected in the upfront fare, and it will be higher than usual. In your application, you will see a comment that the fare is higher than usual because of increased demand.
The price the rider is shown is guaranteed upfront (if during the trip there are not significant changes in the route): so it's convenient for you, because you know exactly how much your trip will cost.
For more information on how the fares are calculated, you can get under: Information on A guide to Uber > After my ride > How are fares calculated?