A good VA should be able to work out a plan with you to both answer the calls and do the email replies.
Suggest: Give him/her a company mobile and ask him/her to work between the hours of, say 12pm and 1pm and 3pm and 4pm (total of 2 hours per day). You can have your company response for missed calls asking customers to leave a message to receive a call back within say 4 hours). The first hour he/she can respond to all the calls in the morning and in the second hour respond to all your afternoon calls and email out the responses.
To be honest if you get a good virtual assistant he or she will probably be willing to carry the phone with them and respond to the majority of the calls throughout the day whenever they can, yet charge you for just the monthly hours you've agreed.
I don't know how many calls you get, but you can assess this with him/her and up the amount of hours he/she works for you if you need to.
For instance I have the outlook email of one of my clients on my phone and check it throughout the day to answer any messages I think are urgent, or respond to any queries he sends me. We agree I work for him 40 hrs a month. My name/mobile is on his company website, so when I answer the phone with my name they are aware I work for him (if it's a personal call for me there's no problem either). To be fair I probably put in a few more hours than I charge him for but the work life suits me and therefore I'm willing to give and take. If the hours start to mount up I flag it with him and we agree additional hours. He can see the work I'm doing for him on his Office 365 account.
You just need a good virtual assistant whose willing to work with you
Most clients use a virtual assistant when they start up and employ someone full time once the company can afford it. So virtual assistants are used to their clients revolving and meeting different needs for different companies.