Just a quick question from someone looking into playing. How long would it take from day zero noob with nothing to become a PvP viable player and actually be able to make a difference on the battlefield?
Short answer: probably not long but totally depends on what you enjoy.
Long answer:
"PVP" is a flexible term in most MMOS; moreso in Eve. Solo roaming, small-group roaming, large-group roaming, organized fleet ops in null, general jspace shenanigans which take a different skill set, faction warfare...
So, your question is: it depends. The learning curve to feel productive as a solo roamer is likely quite long; the learning curve to group up with some guys who know more than you and do some damage and get some debuffs on the enemy? Under a day. Eve has a number of essential tasks involved in any PvP encounter and even a newbie can do something worthwhile. Or at least have fun while failing and try again with no tangible cost involved. Forget about the treadmill or grind of other MMOs; there are literally hundreds of Eve corps who hungrily recruit anyone because the chance of getting that diamond in a rough is worth it.
Diamond in the rough --> player who enjoys Eve enough to develop themselves, i.e., become a better pilot, invest in their character, research optimized fits for specific encounters... or become an FC (fleet commander).
A competent FC is, literally, the greatest asset to a corporation or alliance. A competent FC working for the corporation/alliance is not only a tangible boon on the battlefield but a meta-boon for the collective: they're force multiplying the fun that your other players are having. Eve, like any game, is about having fun and many Eve players tend to suck at that if left to themselves. They need good FCs to show them the light. Many Eve players can name off a handful of names of the most respected FCs in the last decade.
If your dream is to be Solomaster 9000, then it'll take a long time. You need to memorize a ton of shit and have instant recall. If your dream is to fly with buddies and win some fights, you could be doing that tomorrow night.