If you think that "deactivating" within any system erases your personal information from that company's records, it doesn't. All they do is change a database field from "Active" to "Inactive" or migrate your information to a different place in the database.
This is especially true if they have issued you a 1099 in the past. If you've received a 1099, your information is staying with that company for a minumum of 7 years past the date of issuance.
I'd save yourself the hassle and just send all shopping emails to your spam folder/deleted folder/etc.