Yes, you can play "Secret of Mana" without updating the OS on your device. It is also possible to play even if you update the app version, provided you have at least iOS 4.3 on your device.

The following features will also be added if you update the app version, but please note that iOS 7.0 or later is required to use a physical controller.

・Physical controller support
・Retina display
・Option to loop BGM