I updated LinkedIn after informing my boss, my CEO, and close colleagues that I have been accepted and intend to matriculate at an MBA program. My boss, CEO, and one of the close colleagues happen to be my recommenders anyway, so they already knew I was on my way. I only updated after I respectfully informed them of my decisions. This, by the way, did not hinder my ability to continue working at my firm until matriculation. I have good relationship with my firm, and we have understanding that just because I am leaving, it does not mean that I cannot still make tremendous impact for the company before my departure. If you are worried about their knowing your next step, I imagine most of you can make the same argument to your companies, and I can only imagine they will concur.
As for my reason to update, I receive quite frequently LinkedIn job opportunities and recruiter contacts. Out of respect and out of my wish to inform my connections early, I wish to let them know that I will be returning to school and will be seeking different types of opportunities and internships during and post MBA. I think this could a good way to jump start your MBA journey.