Yes it would grow in a pot but soon outgrow it.
The plant is called Common Milkweed (Asclepias syriaca); it grows commonly in North America but rarely has white flowers, mostly they are pink to purple. Very fragrant, and a choice food for monarch butterflies. The plant grows from a very deep horizontal rhizome that could be one to two feet deep in the soil; this rhizome is thick and fleshy and has abundant resources which is why it can drive upwards many inches and burst through a crack in concrete and survive quite nicely thankyou. It will also survive some abuse if it is hard to get at.
Probably the best bet for propagation would be to wait for the seed to set (unless it gets sprayed in the meantime). If all the specimens you see locally are white then chances of cross pollination are low. Seed will be produced in large pods - wait for them to mature and you should find lots of large brown seeds in each pod. You can use segments of the rhizome as root cuttings if you can get to it. Look around and you may find a similar specimen in more open ground that is more accessible to deep digging.
Note that in some jurisdictions there can be a prohibition on this plant - once established in farmland it becomes a real pest because of its very deep rooting, ability to network in large communes. So check on your local regulations.