Does a C# app track how long its been running?

The System.Diagnostics.Process class has a property containing the start time which you can use to calculate how long it has been running:

var current = System.Diagnostics.Process.GetCurrentProcess();
DateTime startedAt = current.StartTime

Use StopWatch class for this feature.

Even if quite overkill, it will always work, even if the user changes the clock or even if there is some daylight saving changes during the process. - Julien Lebosquain (Comment to my answer.)