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Likely, yes. You can kill the next generation off before they are able to grow and flower, however. Just treat the yard again according to the instructions on timing on the container.

This article will offer more information on different ways to kill them off:

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

Grass is always a problem. You need to have a barrier that goes a few inches into the ground to keep the grass from going under the barrier. Just laying rocks or bricks along the edge may not stop it. Here are some ideas:

https://www.gardeningknowhow.com/ornamental/flowers/fgen/flower-bed-edging.htm

https://www.gardeningknowhow.com/garden-how-to/design/lideas/ideas-for-stone-garden-edging.htm

https://www.gardeningknowhow.com/special/spaces/creative-edging-borders-and-more.htm

That might be the quickest option. After this, there will still be things that you might want to do. Treat the area with boiling water over a few days to get rid of any living stragglers. If you can, cover with a clear or black tarp or covering. Many people prefer clear, but black is a second option. These articles will explain in more detail:

https://www.gardeningknowhow.com/garden-how-to/projects/how-to-solarize-garden-beds-to-eliminate-garden-pests-in-the-soil.htm

https://www.gardeningknowhow.com/plant-problems/weeds/boiling-water-and-plants.htm

If they are invasive and you keep them in check, you don't need to remove them. If, however, they are branded a noxious weed in your area and are displacing the native flora, it would be beneficial to the environment to remove them. None of yours mentioned are on the exotic weed list for Illinois. Trumpet creeper is considered aggressive, but not necessarily invasive.

https://extension.illinois.edu/sites/default/files/invasive_plant_species_regulated_by_the_illinois_exotic_weed_act.pdf

https://www.uaex.uada.edu/yard-garden/resource-library/plant-week/gooseneck-loosestrife-7-2-09.aspx

https://www.illinoiswildflowers.info/trees/plants/trumpet_creeper.htm

https://hort.extension.wisc.edu/articles/sweet-woodruff-galium-odorata/

You have some options here. If you want to be sure to kill all the weeds, you can spray the whole area with a glyphosate product and wait about three weeks to give it time to work. (The temperature must be above 50 degrees F for it to be effective.) Read and follow all label instructions.

If you want to avoid chemicals, you can rototill the area two or three times, raking out the weeds and debris between each tilling. The issue here is some of the weeds are likely tough perennial weeds that will still come back if any of the root remains in the soil.

Another option if you are not in a hurry is to wait for warmer weather then solarize it. Cover the area with clear plastic and lay bricks along the edges to hold it down. Leave it in place for several weeks to allow the sun to cook it and kill the weeds.