There is no general rule: you have to discuss it with your pair.
Pair-programming is a pretty invasive practice. You do not decide to invite a colleague into your private space to discuss something. Instead, you are supposed to give up your private space and share your desktop, screen, thoughts, on a regular basis: you work very close to each other. You set up rules along the way by telling your pair what he / she can do and what not. For each pair it is different. Some pairs work well together from day 1, some pairs take weeks or months to find common rules, some never do.
The specific case of email really depends on your pair: some just don't care, some expect you to look away, some will read email during a break so you don't have a chance to see it, and so on.