Yes. BlueMail plays a sound when new email arrives, and you can set a different one for each account, so you can tell work mail from personal mail without looking.
To choose the sound, follow these steps:
Settings | Notifications | [select the account] | Incoming Sound, then choose the new incoming email sound.
On iOS this opens a list of sounds inside BlueMail. On Android it hands you to your device's own notification settings for that account, where the sound sits alongside vibration and the other channel options.
Full steps, including Android's per-app sound and vibration options, are in How Do I Change the Email Notification Sound?.
Notes
- Check you are not in silent mode when checking sound notifications.
- Android can play only one sound at a time, so if you receive notifications on your emails from more than one app - only one sound will be played.