"save" to Gmail? Email them. Open up a different email account, and email them as attachments to your Gmail account.
Or... since you have a Gmail account, use your Google Docs account, and just upload the logs to your Google Docs inbox.
Or... activate your Google Drive account since you have Google Docs, since you have Gmail, and upload them to the common drive box.
If you want all this to happen automatically... install Google Drive on each machine where you use pidgen, and in the pidgen settings, change the directory where the logs get saved to the Google Drive directory on that machine. They won't get tagged with anything custom, but they will be accessible to you from any other machine.
EDIT after more extensive searching, it is possible to do, but with a different IM client to register with Jabber. Once the Jabber account has been created Pidgen should work.
You'll need Psi or another jabber client that supports registering with jabber transports. You'll need that only when registering with the JIT service, you can use any other jabber client afterwards.
You have to add a new Psi account that will let you login to your gtalk account. It boils down to setting your identity to email@example.com, overriding the server hostname to talk.google.com, and using port 5223 (secure). You'll probably get a certificate warning when you connect. Google have an extensive guide with screenshots, you can check that if it doesn't just work for you.
Select "Service Discovery" in Psi, type jabber.anywise.com in the address bar. Google don't have a JIT service so you'll have to use an external one, other jabber servers will work too. You don't need to create a firstname.lastname@example.org account, Google's jabber server will find its way to the JIT service. From the list select JIT, right click and select register. You'll be asked for your UIN and password. Once that's configured you're on ICQ.
To add an ICQ user to your contact list add a jabber user with identity email@example.com, replace 1234 with a real UIN.
If you want to import your complete contact list you'll need the JRU, for gmail.com/googlemail.com it's a bit complicated because I couldn't find how to override the connect server hostname for the perl library they use. Google's talk servers don't support non-secure connections so we have to deal with that too.
What I ended up doing is in JRU I enter username: myusername, server: gmail.com, port: 5224. Then I add a temporary hosts file override that tells my OS that in case it sees the hostname gmail.com it should internally resolve it to 127.0.0.1. I then use socat to wrap the connection in SSL and point it to the right server (talk.google.com). The command is socat tcp4-listen:5224,fork,reuseaddr ssl:talk.google.com:5223,verify=0.
After you modify your hosts file and run socat you will be able to connect to your GTalk account with JRU and use its batch contacts editing capabilities.
You might be able to get away without socat if you can get Net::Jabber::Client to talk secure and use just a hosts override for gmail.com to the IP of talk.google.com.