Yes, e-maktab counts the number of students registered per class as well as per student type. This information can easily been seen by click on the Classroom option at the top and next to each classroom you'll see the total number of students. see image below.
NOTE: To view the student count for student types click Others > Types
You can even print/download a list of all students in a class. To do this you need to click on the classroom name or click on Actions > View
On the top right hand corner you'll see a print button, clicking on the print button will generate a PDF with the all the students belonging to the class.