I've looked through some of the guides available for starting in 20s, and it looks like I'll need to do PvE for decent gear. What if I put on my heirlooms, buy whatever is available on AH, and spam PvP instead? Can I still remain viable given that the gear gap is not so wide between the "haves" and "have-nots" in SL?
I intend to stay in Stormwind forever, spam PvP, and fish while waiting for queues to pop. Would I be too far behind playing this way?
You would kiiiiiiiinda feel behind.
The gear difference is just gonna be too much for you to actually make plays against any half decent twink, who put in the effort you're saying you're looking to skip on.
The class choice(s) also matter a lot in this. Some classes can get away with finessing a bit more, but that doesn't mean gear still doesn't matter, because it absolutely does. I'm just saying that some classes are less restrictive overall.
However, no matter how good you are as a player, you will eventually hit a roadblock where you wish your gear would have been on par, and that's gonna kill you inside. That's at least if you're anything like me, and I can't stress that enough.
I Personally like to push things to the max. If you're okay with limitations and are knowingly aware that you put those on yourself (like, you will literally have no grounds to complain, like, ever), then by all means, go for it. We all enjoy the game in different ways.
It's not like you need go all out crazy to get gear that would put you in a comfortable spot, but doing nothing at all would probably make your twinking experience a not so enjoyable, and most likely, short one.
My advice, be an actual twink. At least put in the bare minimum of effort. Otherwise, you're looking at a bad time.