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Yes, but trace amounts and only for a very short period. Just don't harvest anything from that plant. Let it reproduce and harvest future generations. This will ensure that there are no toxins by the time that you go to eat them.

This article tells about more tasty dandelion varieties and how to prepare them.

https://www.gardeningknowhow.com/edible/herbs/dandelion/growing-dandelion.htm

If you follow the instructions exactly on the weed killer container it shouldn't poison the ground.The instructions should tell you too if there is a waiting period to plant. It's usually just a few days. Some people prefer not to use chemicals and in that case you can lay clear plastic over the area (weigh down with bricks) and let it "cook" for 6 to 8 weeks.
Here's an article with a bit of info about laying sod:

https://www.gardeningknowhow.com/lawn-care/lgen/installing-sod-instructions.htm

This appears to be a brassica, such as wild cabbage. Brassica encompasses a very large group of plants from lettuce to broccoli to beets, and they all resemble dandelion growth to an extent. Eventually, a flower will appear which will differentiate it from other plants. If the leaves bleed when cut, or have a particular smell, then this can narrow things down some.

https://www.gardeningknowhow.com/plant-problems/weeds/cruciferous-weed-information.htm

I wouldn't even consider using anything that has had contact with any poisons at any point, ESPECIALLY with someone who is not well. This will do more harm than good.

Either purchase some that has been grown in proper conditions, or be sure to take from an area that you know FOR SURE is clean. There are too many risks with consuming these types of toxins, even for a healthy person.

You'd have to know what the area's been treated with and what kind of soil you have. Some herbicides break down quickly; some pesticides can take up to five years. You may want to contact your local university extension service for more information. There is no way I know of to test soil for chemicals at home, but perhaps they will know more.
I hope these links will help:
https://www.gardeningknowhow.com/extension-search
https://www.canr.msu.edu/uploads/234/68557/rec_chem_soil_test_proce55c.pdf

You could raise the dandelions in a raised bed that you added soil to if you don't particularly want to eradicate them from your yard.

Since they are in the area, anyway, it will be a very difficult thing to do. Aside from, very constant, handpulling, there will not be much that can be done.

https://www.gardeningknowhow.com/edible/herbs/dandelion/dandelion-control.htm