Hmm don't think so unless maybe you have your notification volume set really high.. But I have never heard of anyone saying that other people on the other line could hear their notifications it would be a odd thing to happen..
The other party should not hear your notifications but if your phone, like mine, is typically set to Vibrate instead of ring, they might hear a slight buzz when the phone vibrates.
Example: I talked to my daughter in Colorado just about every night either on the phone or via Skype. I can sometimes (not always) hear a little buzz when she gets a notification.
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