Without an SD card, the root will have limited value, but you might be able to get your sync working alright. You can get apps that help you kill extraneous process. You'll probably want to go in and remove all processes you don't want and can safely remove. In fact, this is essential if you want to have a decent batter life. I think Titanium Backup will help you do it, though I did it manually with root explorer. In fact I'm eyeing up a system cloud process at the moment that's using 10 meg. Maybe it can be destroyed
But read carefully and read up about it all.