I do not have the option to stop BA sync.
When you initially setup the phone you can skip the setup process. It's like the first thing that pops up after the "activation" sequence. If you set it up in there, but want to turn it off now, you should be able to under [Settings > Accounts & Sync].
FYI, I've noticed that this process runs in the background even if you aren't using it. Rather than risk deleting it, I used
MyToolbox to "Freeze" it. This disables app--without risking a resonance cascade inside your phone because you deleted something important--so it can't run in the background. MT is made by Rerware, the same company that makes MyBackup Root/Pro. I'm pretty sure buying the Pro version of MyBackup (Root version is free) gets you a free license for MyToolbox. TBH, I haven't yet decided that Pro is worth paying for, but Toolbox is definitely worth the $2.
You can batch uninstall/clear cache/clear data/(un)freeze/restore market link/break market link/force close any application(s). The restore/break market link is really nifty. Say, after restoring your backup, you can't update an app because the market doesn't recognize the app as being installed, this will fix that. Likewise, if you install an app and you DON'T want it to update, you can break the market link. This will work on system apps too, if for some reason you didn't want YouTube, etc. to update.