Yup, it can! On the app's settings there are separate sections for Caller ID and Contact Sync, as well as Birthdays. You can enable/disable each one separately.
On the Contact Sync make sure that you select the appropriate sync options like frequency or if you'll only allow the app to sync over WiFi or when charging.
I like it because it works even with people I don't have on Facebook (as long as their security settings allow it, of course, but if they didn't, then it wouldn't work on the 'native' one anyway).