Yes, it's simply a perfective of слышать and yes, it can also mean "to overhear" or happen to hear as you put it. Note: it's in no way different from usual слышать rather than its aspect, the meaning of overhear or happen to hear comes just from the fact of getting to hear something, doesn't matter how you did it. The only Russian verbs I can think of, that are derived from слышать and which actually take into account how you happened to hear something are:

выслушать - hear someone out, to listen to everything a person has to say;
подслушать - to eavesdrop, to listen in on a conversation secretly.