Often, new starters are excluded from 360 degree feedback.  The reasoning goes that they are too new for others to have formed a valid opinion of them.  At the extreme of the first few weeks, I agree.  But, after a few months I believe that tailored 360 degree feedback would be very helpful. 

People are forming impressions of you very early - some of those impressions will stick whether they are valid or not.  The earlier that you can get useful feedback the sooner you can tackle the impression you are giving.

If you consider introducing 360 degree feedback for new starters then you should of course take care on the questions - perhaps a full competency framework would not apply yet.  But, consider using 360 feedback as a tool around the 6 month period.

Brendan