Not that I know of. The Ring/Silent switch is designed that way so users can easily play games when in a place where sounds might annoy other people. Why not leave it on?
Here's what it mutes and doesn't mute.
What the Ringer Switch Does Mute:
•Phone-call ringtones
•Text-message alert tones
•Notification alert tones (from iPhone apps and third-party apps)
•Calendar alerts
•Reminders
•Camera sounds (snapping a photo)
•Game music
What the Ringer Switch Doesn’t Mute
•Alarms from the Clock app (example, setting an alarm to go off at 6 am).
•Timers from the Clock app (example, setting a 15-minute countdown timer).
•Audio from the iPhone’s Music app (example, playing the Beatle’s “Hey Jude”).
•Audio from the iPhone’s Video app (example, playing an episode of Lost).
•Some audio from third-party apps like streaming radio, video, and music (examples, playing a radio station via the TuneIn Radio app or a video in the YouTube app).
•Tones when tapped in the iPhone’s various settings (for example, when changing your ringtone or text-message alert tone) and in the Clock app (for example, when selecting what sound the iPhone will make when the timer runs down to zero).
•Tones when changing the volume of Ringer and Alerts in Settings–>Sounds
•A sound alert when sent from the Find My iPhone service.