Hmm, I don't think so. This is my gut reaction not based on a study, but what you said already points in that direction: 1 influenced vs. 20 annoyed seems like a net loss. This is not even counting the opportunity cost from what you could be doing in the same time (although you could argue the copy and paste is nearly instantaneous).

I may be letting my personality influence my assessment, but I think that the general rule of not doing devious things to promote your cause is almost always best.

Eliezer:

We don't live in a righteous universe. And so, when I look over my history, the role that my ethics have played is so important that I've had to take a step back and ask, "Why is this happening?" The universe isn't set up to reward virtue—so why did my ethics help so much? Am I only imagining the phenomenon? That's one possibility. But after some thought, I've concluded that, to the extent you believe that my ethics did help me, these are the plausible reasons [...].

Here Eliezer is mainly talking about truth-telling, but I think the same phenomenon can be seen in other attempts to game the system.

There are lots of other forums where you could legitimately share info about animal suffering. For example, there are tons of groups on Facebook where people can post links. Maybe university groups, atheists/freethinkers, philosophy groups, etc. (Is there a reason you're not on Facebook yet? )

Outside of Facebook there are other venues, too: You can find forums for these kinds of activities (though registration isn't always as quick as on Facebook), or answer relevant questions on Quora, or reply to people on Twitter, etc.

Let us know if you have thoughts on these. It is slower to post in these places, especially when you aim to make the post not sound like spam, but it's probably worth it. Spam could easily have negative expected value.