Hopefully you and your academic advisor have built a rapport with each other. But, you should be concerned if your advisor knows your GWID by heart. This means that he or she has a photographic memory and should be putting this talent to use in some other way. Or it means that you require so much attention that it is easier for your advisor to commit your GWID to memory. Neither option is good.
It is important that you include your GWID in messages to your academic advisor even if you and your advisor have a strong relationship. Including your GWID helps your advisor file your communications properly and investigate questions you might have related to your student record. Remember GW was founded in 1821, so chances are that there are a number of students in the GW system with your same name. The GWID is the best way to distinguish between you and them.