That's neat, I did not know about the possibility to pick poses with the MHX2 plugin. Very useful...or rather it would be if I could figure out how to make it work correctly. For me, the pose picked in the MHX2 Runtime panel seems to give a result relative to the starting pose of the model, or in other words the bone rotations are added to whatever pose was exported from MakeHuman. However, exports with either the base pose ("none") or the T-pose both make the shoulder bones end up with rotations different from what they should be as compared to the pose in MH.
The latter example looks closer to what it should be but the elbows are fully extended and the upper arm bones have a bend backwards and inwards which just isn't right. Am I doing something wrong with the export or import?
About the poses themselves, as viewed within MakeHuman; they do look quite natural, but mind I do not have any professional knowledge on human physiology, I can only speak from personal experience and informal studies. Anyway, the 3 poses you mention are interesting because besides having the shoulders rotated to bring the arms above the chest they are also like snapshots from the middle of a continuous motion instead of static poses. Even the gym pose is not balanced, it would have to be going up to a handstand or down from there.