Question

In a car accelerating on a level rod is archimedes' principle valid

Answer 1

Archimedes principle is dependent on the frame of reference there may be irregularities but the concept doesn't change
As you can see in attached doodles acceleration affects force applied by water on the wall, not on the bob.

For a person in car Bob just displaces the water however for a person outside the scene is pretty much different as forces due to acceleration also act in vector form.