The shock cord has several purposes. It is designed to be the weak point in your system so it should fail before your tarp rips in high winds. I don't know for sure, but I would think you're going to have a lot of other problems if there's enough wind to break the shock cord. It also serves to keep the tension you want on the tarp as the nylon stretches.
To answer your question, no you do not need the shock cord but you loose the functionality listed above.