Within reason of course. I mean that’s the whole reason the Policy Enforcement Team(PET) exists. Yesterday Marc Whitten announced a huge change to the Xbox LIVE Code of Conduct.
Of course the use of racial slurs and harassment will always be against the CoC but you now have a little more freedom to your gamertag and profile. They do warn that these changes may take time to go into effect so just be patient.
I feel this is a step in the right direction for Xbox LIVE. It allows more freedom of expression among users. It also means that they will need to step up the enforcement team. They will need to take complaints of harassment seriously and in a timely manor. There are players out there who go around harassing people for months before the PET gets to them.
For this new change to the CoC to work Microsoft must be ready with new additions to the PET. There are too many people out there that cause damage. They need to be dealt with quickly and efficiently.