No. No. No.
You must provide level shifters.
There are several 40-pin adapter shields. They have onboard level-shifters. You can buy them locally in Europe. Delivered in 24-48 hours.
You can use jumper wires from 32-pin to 40-pin.
This particular Adapter has 40-pin and 32-pin socket. If the 32 pins match your display, it will plug and go. It is made by CTE or Sainsmart. If you receive a Sainsmart pcb, check it carefully for bad soldering etc. Check pin#1 for 3.3V
If you connect 5V to your 3.3V display you will damage it. The Blacksmith does not put his hand into the Forge. He uses tongs.
David.