In light of how many cookie-cutter applicants are out there, I think your story could make for a great personal statement. It would definitely distinguish you from the pack. The tricky part is to make sure it distinguishes you in a positive way -- which is definitely possible, but hard. Out of curiousity, can you submit an application without telling that story? That is, were you formally sanctioned by the school, or did they just ask you to leave voluntarily? If you weren't formally sanctioned, you might consider holding back the details and playing it a little safer. You can still talk about your drug policy reform aspirations, but you might present it a little differently. If you have to disclose what happened, then you should 100% own it and proudly tell the whole story in your personal statement, explaining how the experience solidified your resolve to become a lawyer. In any event, you sound like a very interesting applicant!
By the way, I was also in SSDP as an undergraduate...