No. JCL really cannot do anything. . . All JCL does is execute programs - one way or another.
What you want to do is not a subject for beginners/students. Many quite qualified people would not be able to automate this quickly.
One way to do what you want is to write some rexx code, invoke sdsf, and determine if the named job is in the system or not. If it is in the system, is it running, is it completed (successful or failed), etc. What to do if there are multiples of the named job (lots of jobs run several times a day/hour).
Hope this helps,