Hi NikAssist:
Sorry I don't know your name, but I currently offer email management to my clients. There are some that I respond to emails on their behalf and then there are some that I review emails, filter out the spam, and include the important ones on a list throughout different times during the day.
This way a client can review the important emails and either a) assign the task to you as a VA to follow-up on or b) he/she can respond to the email.
I think as far as responding, it may take awhile for you to build trust with the client since you are in fact responding on his/her behalf. All of my clients who I process email management for - I only respond 2 out of 3 for. And of course, there is another service in which if they "try" to manage 10-13 email accounts in one day - you can always sort those into folders and organize for the client.
Good luck and let us know how it goes.