Weedy, yes. And how do you propose to keep them from
seeding? BTW, several species (don't recall which off the
top of my head) are considered noxious weeds in some
states, which could get you in some hot water in some
circumstances.

The enforcement of federal and state noxious weed laws is a difficult
challenge in the midst of so many other enforcement challenges.
Nonetheless, to be safe you should look at the EWIRM database for
official and unofficial weeds lists and images in your state or
province. EWIRM from Ergonica sorts over 200 weed identification
references by US state or Canadian province.

Ray
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EWIRM: Nature makes plants, humans make weeds!