The problem with amember is the source code is proprietary. To create an integrated plugin someone would need to modify it. Their license doesn't give permission to modify the code even for personal use, and it doesn't give permission to distribute modified versions to others. Some of their revenues come from selling plugins which integrate amember into other software: Invision Board ($40), vBulletin ($40), and ListMail ($40). I kind of doubt they would allow their free version to be integrated here and then given away for free, but you can always ask and see what they say.
The other problem is when you integrate something into GPL code where it is calling routines and sharing tables it is considered part of the whole program and thus must be licensed under GPL or a GPL compatible license if it's distributed to others. I doubt amember wants their code to be GPL. To retain their more restrictive license would require approval from the copyright holders of Geeklog.
So, if you want this done you'll need to get two sets of approval. If cgi-central doesn't care if their modified code becomes GPL, then you just need one -- theirs. Of course, someone could just create their own with a similar capability and not have to get anyone's permission.