Yes, in US English the word "cooperate" has a distinctly different
meaning than it's literal definition. It is more congruent with
"comply", "submit" or even "surrender".
With that usage, of course head-down position looks more
subservient. A person who is fearful, or surrounded by a generally
hostile population might perceive that as "more friendly" at a stretch
of semantics, but that would say more about the culture and context.
My experience is quite the opposite. Heads-up with eye contact
indicates an engaging personality, readiness to listen and see, and
therefore a more sociable outlook. First thing you get taught in
cadets or scouts or whatever is "heads-up!" - a ready/attentional
posture.
Indeed, the widespread problem with smartphones is visible in any
British high-street. People bimbling along, heads-down, necks craned,
staring into the 6 inches of virtual reality through which they see
the world. It's not only horrifying from the POV of their health and
safety, it sends a "non-approachable" signal.