An excellent post, if I may say so. (And yes, they all connect to the "low side" port). The "High side" will be several hundred PSI with the pump running, so nothing will leave the can - quite the opposite, in fact)! The low side, at the point just after the compressor cuts in, will only be a few tens of PSI. On some systems, it can be very low indeed - close to atmospheric pressure, in fact. That's one of the problems with these "one-size-fits-all" gauges that have a green zone on them. On pretty much every "healthy" car I've tried one of these gauges on, the topup can gauge has either told me it needs gas, or it has been right near the bottom of the green zone.
Lastly, some people stand the top-up bottle in a bucket of hot water (especially as the can starts to get closer to being empty), to encourage the gas to leave it.