Yes it's possible to hear yourself snore.... your own snoring can wake you up out of a sound sleep.... trust me been there done that. :)
I have been awakened by my own snoring a few of times over the years. It was always when I was congested with a cold or flu.
I rarely snore
It can happen but my guess would be it would be more of "lack of oxygen" waking you up rather then the sound of a snore. But I could be wrong.
Clogged up by a cold, I can hear my own snore in my sleep.