There is if you use the alarm app, Gentle Alarm. Besides the plethora of amazing features that app has, you can also turn off the notification bar icon and the app still runs in the background just fine. I've been running it that way for a long time.

On a semi-related note, my favorite feature of Gentle Alarm is the ability to keep alarms scheduled, but skip as many of them in order as you want. That way if you are on vacation for one day you can turn off scheduled alarm(s) for just that day and not be annoyingly woken up. I was on vacation for a week and was able to turn them all off and the following week I didn't have to remember to turn my alarms back on, already taken care of.


No, for the same reasons detailed in this answer.

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

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