Does the Palestinian authority actually represent the will of the Palestinian people ?

Like any other society, Palestinians are not a monolith. The Palestinian intellectual and political tradition has had a long history of dissent and debate. However, Palestinians in general hold a negative view of the Palestinian Authority and the Oslo accords. Many have come to view the current Palestinian Authority as subcontractors for Israeli control of Palestine, especially through its security coordination.
So, No.
Further reading:
Myth: The Palestinian Authority subsidises “Terrorism” (Pay to slay).