If drag racing happened yesterday, would it be drug racing? No, that’s not right, though there’s definitely a bad pun of a book idea somewhere in there.
Using “drug” (as a verb as well as in other forms) can cause some issues. Sure, it’s commonly used in the South and Midwest, but unless you’re writing a regional piece or giving a character a distinctive speech pattern, stick with the standard form of “dragged.” By using the correct word, readers—regardless of their geographical location—will stay with you. The last thing you want your readers to do is pause and debate your word choice, right?