Hey everyone! I rooted my PlayBook the other night, and found that Accounts & Sync had been disabled by RIM. I was very disappointed in this because I have everything Google in my life.
However, I found a way around it! It does not auto sync, but you can do it as often (or as little) as you'd like.
From your launcher, open Dev Tools.
Scroll to the bottom and open Sync Tester
Choose your application from the drop down list (i.e. contacts is "com.android.contacts - com.google)
Choose 'bind'
Choose 'start sync'
Select your Google account, and it will sync and all will be delightful!
I've gotten it working with Contacts, Picasa (in Gallery), Calendar, Twitter, Gmail, Books, Music, and Currents.
Also, if you load the Google Music APK (which I've attached since it doesn't show in the Market), it launches but always crashes when going to the default view (recent, artists, albums, genres). If you launch it from a widget on the home screen, you may have more luck. When it opens, it works just fine. Until you're stuck on an album and you can't get back to "All Music".
How did you get it to see your Google account though? Im not able to enter it anywhere in the ANdroid menu, and when I follow the process you described in Dev Tools in ICS Launcher and bind etc, my Google account doesn't drop down anywhere (presumably because I haven't had chance to input anywhere). Any ideas?