I accidentally sent a message to a person on Facebook, and that person is not a friend of mine on Facebook. After I realized that I scheduled my profile to permanently delete in the near future.. So can a person will be able to hack my profile even after I deleted it?
No, once your account has been deleted permanently no one can hack the account.
Once you choose to delete your Facebook account permanently, all your data will be deleted immediately from everywhere including Facebook servers permanently (few data takes around 90 days to be deleted from the server), so there's no way to regain access to your account and the data associated with it.
Hope you have not sent your account credentials to the person accidentally, if so change the password immediately. After that delete your account.
Learn more about Deactivating & Deleting Accounts.
When you delete your account, people won't be able to see it on Facebook. It may take up to 90 days from the beginning of the deletion process to delete all of the things you've posted, like your photos, status updates or other data stored in backup systems. While we are deleting this information, it is inaccessible to other people using Facebook.
If you sent a message to someone you don't know on Facebook it doesn't mean they can hack to your account so there's no need to delete your account unless you sent you password in that message.
If you did so change your password immediately from your Facebook settings and then you can delete your profile if you want to.