If you have one action token and you push to become the pilot, do you take the push click or not since at the end of the action you are off the board?

You take pushing damage as normal and may also use effects like willpower to ignore that push damage. You also clear as normal while being off the map.

EDIT: From the Rules E&C over at WIN:

Thanks just was a litt confused on timing

Turn one, move next to the Turtle Van.
Turn two, take the action to enter the van, take the token, push to click #2

Turn 3 - even with the two tokens, the van can use your AV and DV and power (P/PB). You clear while piloting the van.