In the case of async/await methods, the Task will already be started. AFAIK, all the BCL methods added for Task-based versions return already-started Tasks. It would be kinda weird not to, since the common consumer case is now:
var foo = await GetFooAsync();
[EDIT] Based on Stephen pointing out that the TAP guidelines covers this (and he already includes a link to the guidelines), I'll include a quote of the relevant bit from page 4 (in The Task-based Asynchronous Pattern Defined -> Behavior -> Task Status), and I've added bold+italics around the key parts.
Task Status
The Task class provides a life cycle for asynchronous operations, and
that cycle is represented by the TaskStatus enumeration. In order to
support corner cases of types deriving from Task and Task as
well as the separation of construction from scheduling, the Task class
exposes a Start method. Tasks created by its public constructors are
referred to as “cold” tasks, in that they begin their life cycle in
the non-scheduled TaskStatus.Created state, and it’s not until Start
is called on these instances that they progress to being scheduled.
All other tasks begin their life cycle in a “hot” state, meaning that
the asynchronous operations they represent have already been initiated
and their TaskStatus is an enumeration value other than Created.
All tasks returned from TAP methods must be “hot.” If a TAP method
internally uses a Task’s constructor to instantiate the task to be
returned, the TAP method must call Start on the Task object prior to
returning it. Consumers of a TAP method may safely assume that the
returned task is “hot,” and should not attempt to call Start on any
Task returned from a TAP method. Calling Start on a “hot” task will
result in an InvalidOperationException (this check is handled
automatically by the Task class).