Previously locked Galaxy S3 root

[Kiot Poi]

Hello everyone, excuse me for being a newb to rooting, but here's my question: I purchased a used Galaxy S3 locked to Orange UK, unlocked it immediately (it still shows the Orange branding when booting up though) and the battery drains really, really fast, which I suspect might have something to do with the carrier's bloatware still running and not showing up in Applications Manager's list. So far only one app showed up once - some kind of contacts sync and it is not on the list so I can't uninstall or disable it. So before trying to root :-\ - is rooting previously locked phones any different to normal rooting? I tried searching for this but there doesn't seem to be anything about it.