Well, maybe there’s a benign motive to it, but I see a couple bad points about doing so.
1.) The more influential and well-reasoned the person who responds to Phelps, et. al., the more credibility is lent to them. It’s analogous to why Gould refused to debate creationists and ID theorists, because he feared that to do so would lend those people and their (IMHO, and in Gould’s NSHO) looney and nonscientific theories credibility. If we take Phelps seriously, that is to show that Phelps has a serious position. If we take time out to mock him or get angry, that shows him that he has the power over us to tick us off.
2.) Sometimes the process of expressing outrage at these people brings out the worst in us. I’ve seen some of the most hate-filled vitriol ever encountered on this message board done in the name of pitting Chick or Phelps. Do they deserve it? Maybe. Should we allow them to make us so angry that we respond with hateful invectives? I don’t think so. Life’s too short to spend too much time filled with hate and anger at anybody. If Phelps and Chick don’t realize that, all the worst for them. For us to become filled with seething hatred at them is to make the same mistake, even if the only people harmed by our actions are ourselves. Yeah, they’re worse, but I’m sure their lives can’t be that great if they spend most of it holding onto anger. Let’s take a lesson from that, and realize that our own anger isn’t doing us any good either.
IMO, the best way to fight these people’s influence on those who are yet ignorant on the subject is with cold, reasoned, simple arguments in GD. Pitting them might make you feel good in the short run, but it only gives them more power over you when you succumb to your anger, and it does nothing to fight their messages.