Does the human abdominal cavity use pressure to maintain posture?
I found this review which can help to clarify this notion of intra-abdominal pressure : Intensive Care Med. 2009 Jun;35(6):969-76. 
What is normal intra-abdominal pressure and how is it affected by positioning, body mass and positive end-expiratory pressure?
De Keulenaer BL1, De Waele JJ, Powell B, Malbrain ML. 
The authors mention that there is indeed a positive pressure in the normal subject. This IAP is contributed by gravity, uniform compression (abdominal contraction, diaphragmatic contraction, mechanical ventilation, rib cage excursions) and shear deformation, this last one depending on the intrinsic stabilty of the tissue.
The authors conclude that "the abdomen behaves as a hydraulic system with normal IAP of about 5–7 mmHg..". Kind of a can of soda, without the bubbles...
Pathologies affecting this pressure are named "abdominal compartment syndrome) and result from multiple etiologies (obesity, trauma...,).