Yeah, it's an amplification! But as you said, firstly you need really good "skills". Altho' I would put in the set of "skills" something that a lot of people lack and don't spend their time perfecting, and that's authenticity, clarity and sincereness. If a person is developing his "craft" in playing, writing, any art form, a lot of people neglect the aspect of discovering their unique language, and for that it takes a lot of time and a lot of experiments. Because as you go further in discovering the arts you read through the mystique and manirisms. And at that point it depends what is your focus.
For me, I mostly catch on to musicians and art that is authentic and vunerable, where the feeling cuts through the bullshit (most of the time - it's the show). But those artist tend to stay (by their own choice or not) on one level of "success" because rarely authenticity beats mainstream... But it has always been like that i guess...

At the end of the day, I think it just depends on your focus - what do you want to do... If you wanna be a session musician and play with a celebrity band then you have to chase it, not just play in your town, but move to somewhere bigger and be persistent (I've met an amazing drummer called Larry Belton Jr. who moved from Sacramento to LA and after a couple of months he started playing with some better musicians on jam sessions, and one of the bassists was a bass player with Jason Derulo - and guess who's the drummer in his band for the last couple of years ;))

But if you want to focus on the music and style, then I think it's counterproductive to "make it big" because that kind-a makes you being in a rut and subjective towards your music, and I guess you're "more afraid to make mistakes" which is not good for the whole process of discovering stuff about your art.

Any connection is as good as you use it.. You can do good just by a word of mouth if you're unique and of quality, but it can really help if you're in a position to use your connections without making big compromises - and there are always some.