This is a standard and every semi-smart spammer can strip the "\+.+" part so it works only with legit websites that you want to handle in a special way.
another options is to buy a domain with a cpanel and set up a forwarder and filter to a specific folder in your secret main email account. The extra benefit here, since you own the domain, is that you can create a send identity of your arbitraryforwardingaddress@yourdomain.tld
