No, in all kinds of environments, from hunter gatherer to agrarian to urban.
Just because you grow your own food doesn't mean you have enough of it. Being a farmer might mean that you're going to be able to squirrel away more food than someone who is similarly poor and living in a city, but it doesn't mean you have infinite food.
So there goes your glorious past where sex and pregnancy are wonderfully linked and everything was sunshine and rainbows until these things "became decoupled".
I wouldn't say sex and procreation are completely disassociated as *signifiers*, but I'd say they are moreso than they were before, and that this sundering is progressing.
Good. Maybe people will stop having unwanted kids and pregnancies they don't want then.
That actually also depends on the society.
It's true across the board. If you didn't own anything in an agrarian environment, it was almost always because you were a either young man and a day laborer, or a slave, and I don't think slaves cared much about controlling birth, if they were even allowed to.
Uh, you claimed that all poor people owned property. First of all, serfs generally didn't own property (maybe some of the very few who were free did) and for some time in many places, serfs or slaves made up most of the population.

