Yes, but you still need frequently check your Brooklyn College email account since many important and time-sensitive messages from CUNY (e.g. Blackboard, Cleared4, and more) are only sent to your official college email account (@bcmail.cuny.edu).
How to set your personal email account
You can provide Brooklyn College with a personal (preferred) e-mail account in WebCentral that will be used for internal college transactional messages. Go to My Info > My Personal Info > Personal Email to get started.