Well that's the great thing about Eve. The way it's designed, a brand new player can be effective. Not as effective as a player who's played for years, no, but still effective.
I started playing Eve a couple years ago, and my second day ever playing, I got invited into a fleet made up of nothing but complete newbies and a fleet leader who'd been playing maybe 6-8 months. There were about a dozen of us, and we headed out into low-security space (good PvP area for small groups) and proceeded to kick some ass. We killed more ships than we lost, and every ship we killed was worth more than all the ships we lost put together.
Focused training for about 18-24 months is sufficient to get you to an expert status on just about any ship battleship-size or smaller.
That being said, Eve does have its shortcomings. For me, the gameplay itself ended up being just too boring. It's all just click-to-move and then click to activate or deactivate modules. The strategy and tactics (both in warefare and economics) is where the real fun is at, so if you enjoy that kind of thing you may just find Eve is something you really like. In the end I just wasn't enjoying it enough to justify the subscription cost, so I finally quit after a year and a half.