Android - Hide Alarm icon in the status bar

On Android Marshmallow, you can use the hidden System UI Tuner.

Open the quick-setting panel, then press and hold the Settings' cog wheel until it starts spinning. You then get an additional settings entry in System > System UI Tuner > Status bar, where you can hide the alarm.

No, for the same reasons detailed in this answer.

Can I hide a program from ongoing activities in the notification bar?

Easiest way if rooted: You can use GravityBox, to hide the Alarm-Clock-Symbol.

1. Open the app.
2. Go to "Adapt Status Bar" (I don't know the exact English translation)
3. Choose "Adapt Clock"
4. Tick the box next to "Hide Alarm Symbol"