It depends on the context. My boss is so busy that he rarely answers to my emails, he is available to talk very rarely (once every few months) so I write him what I plan to do then I do it. He never answered "no". Even for vacations, I just let him know when I go and for how long, if it is up to a week. I am responsible of my own work and he is just around.

My former manager used to do the same. He is a 40 year veteran, retiring in the next few months and for the past 6 years since I met him he wrote many emails telling people what he plans to do and just did it. It works for us very well.