Are either parent also applying for British citizenship?
He can register, but there is a general expectation that one of the parents is also applying for naturalisation at the same time. He may want to put some thoughts into arguing good reasons on why he should be registered and how his "future clearly lies in the UK" when his parents (at least one) are not being naturalised.
Have a read through
Nationality Instructions - Registration of children, particularly from page 27 onwards.
Page 28 of the document above states
It will rarely be right to register a child neither of whose parents is or is about to become a British citizen. However, each case must be considered on it’s individual merits and there may be exceptional circumstances to justify registration in a particular case such as:
• older children (16 and above) who have spent most of their life in the UK or children who require citizenship to follow a particular career such as in the Armed Forces
• the child’s future clearly lies in the UK
• the person making the application has day-to-day responsibility for the child’s upbringing and is, or is about to become, a British citizen
It is worth remembering that both registration and naturalisation for your brother is at discretion and he could be refused.
I am not a lawyer or immigration advisor. My statements/comments do not constitute legal advice. E&OE. Please do not PM me for advice.