I'm sending almost all the spam I receive to SpamCop via SpamAssassin. But I think reporting the spam to the ISP is not so useful: there are so many spam-friendly ISPs around the world that it's like emptying the ocean with a tea spoon.

What I want is just to contribute to the blocklist effectiveness, as I benefit from it myself and my little site.
Is it necessary to pass through the boring reporting step for my spam to be considered in blocklist updates, or is it sufficient to send the spam to SpamCop special address?

Your complaint is not "registered" with spamcop until you complete the reporting. If you complete the MailHost configuration to minimize the change of reporting yourself, you should investigate quick reporting in the FAQ here. That only sends reports to the source of the message, not any spamvertized sites, but requires no additional effort to complete the report.

...The Quick Reporting FAQ is at URL http://forum.spamcop.net/forums/index.php?showtopic=163. Please take special note of the WARNING. It is because of that warning that I do not use Quick Reporting, especially since my e-mail provider has added and switched IP addresses on routing servers in the past, causing me to accidentally report my e-mail provider!