The Worst Invasive Species in the Midwest You Oughta Be Killing

Yes. Like he says, you want to get the herbicide into the plants roots so it kills it. If you don't, plants like this will just regenerate from their carbohydrate stores in their root systems.

With thistle, they try and spray right before fall for this reason

Small infestations of young plants can be pulled effectively by hand. For larger plants in low-density invasions, a root-wrenching tool or hoe can be used to remove the majority of the root system, which the plant will not recover from. Mowing is an option when removal of the shrub canopy is desired and eliminates the need to drag and chip or burn the stems following cutting.

https://extension.psu.edu/buckthorn