There doesn't seem to be a way to subscribe without receiving the email alerts. Honestly, that's the original point of subscribing - phpBB was created long before push notifications, so it was the only way for the system to notify you.
The latest version of phpBB (3.1.x) has a new 'notifications' feature which gives you a little more fine-grained control over subscriptions, including what kind of alert you get - either an email, an in-forum notification, or both for various actions. I could easily see them adding an additional column for push notifications to a phone number in the future, but for now it's just the email or in-forum notification.
I know Ice has intentions to upgrade sometime in the future but not until there is more support for themes and mods/extensions - 3.1.x is still relatively in its infancy.