Imagine you fill up a barrel with water (or any other liquid) dig a small hole at the top and place a sufficiently large straw in it, so that there is no pressure loss or anything. Then you start to pour water in the straw. Is there a critical height at which the pressure at the level of the barrel is so big it would break it apart?
Yes, you can blow up a barrel using the hydrostatic head in a long vertical straw hydraulically connected to the barrel. But... you have to ensure that the straw and the hydraulic connect to the barrel are both strong enough such that the barrel acts as weakest point. I'd say the word "straw" doesn't do justice to the thick-walled metal tube you would need to deploy.
Relevant theory can be found here.