This is a debate among many online instructors. Some say time tracking is a vital feature in an LMS, others say it is useless information and cannot be the basis of a grade.
The problem lies in what can be tracked: time spent in the course. The students might be logging "time" but not interacting with the material. They could be playing video games.
That said, there is usually a way to get an idea of your students' activity level in the course. This will vary by LMS, but using Moodle as an example, you can get a general idea by viewing the Activity Logs.
In Moodle, if you click on a student's "Activity Reports" tab (accessible in the student profile), then on "All Logs" you will see something like this:
Wed February 1 2013, 08:43 PM 188.8.131.52 TestStudent2 scorm pre-view 1421
Wed February 1 2013, 07:53 PM 184.108.40.206 TestStudent2 scorm view Topic 1: Algebra—Everyday and Extraordinary
Wed February 1 2013, 07:53 PM 220.127.116.11 TestStudent2 course view Algebra 1, An Open Course (Sem 1) -
Wed February 1 2013, 07:53 PM 18.104.22.168 TestStudent2 assignment view Unit 1 : Lesson 1 : Topic 1
Wed February 1 2013, 07:51 PM 22.214.171.124 TestStudent2 course view Algebra 1, An Open Course (Sem 1) -
Wed February 1 2013, 07:50 PM 126.96.36.199 TestStudent2 scorm view Topic 2: Solving Multi-Step Equations
You can see where they went, and how long they stayed in any given place. In the example above, the student spent one minute in Topic 2, which could indicate that he did not do the work -- or that he had trouble getting it to load. He also spent 50 minutes in Topic 1, but we do not know if he was struggling with it, watching it multiple times to "get it", or completely distracted and not interacting with it at all.
Because of these limitations, many teachers decide to grade based on learning, proven by scores on quizzes and homework assignments, rather than by time spent.