Yes — you will still receive notifications for new incoming emails even if the app isn't running. These are called push notifications.
Whether instant push is available for a given account depends on the account itself: it is not offered for POP3 accounts, some providers switch it off for their own servers, and on Android it is offered only for accounts you signed into through the provider's own sign-in page rather than with a password. Where instant push isn't available you can still use Frequent Fetch, which checks for new mail on a schedule. See notification methods.
For more info about Notifications tap Here
