So yes it's possible and it's even one of the most fun part of Eve.
So he had two Formula 1 but the real key to his success was because he knew each law of the world and he was a master when he fought. It is one of the best point of Eve, you can have a Formula 1 but if you don't have the experience to use it, you will die at the first engagement. And at the same time, when you are excellent you can engage enemies even by being outnumbered by 10, and this is awesome.
(Another key point on Eve is: each ship have different size with different role. It is like to have catapult to greek titan in World of Warcraft. And even with one of most hardest task in any games, Eve stays balanced and coherent for a 800 vs 800 as well as a 1 vs 1 with different tactics at each size)
There are many many things to know in Eve. For instance, only after 4 years I could say I started to see the whole thing in PvP. If you want to see "Hackers" in Eve at fleet level, you have all the Rooks and Kings videos. [1][2] For lone rangers' videos, you have the Garmonation series, or Eve is Easy's video [3], and Darkness' videos with the Dark Perspective 3 and 4. [4]
[1] http://www.youtube.com/watch?v=Xwql_Sp0QG8
[2] http://www.youtube.com/watch?v=XrYe_4vHzgE
[3] http://www.youtube.com/watch?v=TcRAx-uwk40
[4] http://dl.eve-files.com/media/0904/Dark_Perspective_4_final....
It does hinder your ability to participate in big battles like this and money making will be slower. But some people don't mind since they just want to be independent.
But you can run a small or even solo pirate operation, preying on lone travelers. Or run goods to dangerous markets in stealth transport ships. Or in a much much larger, much more expensive jump transport ship (just don't get ambushed!). Or start a manufacturing operation. Or for the truly hardcore (and really best done in small groups) go make a living in a wormhole for a month or two.
There are nearly countless things you can do solo or with a small group. The easiest way is to be part of a large alliance and have "safe" space to operate from - this does not, generally, mean you have to follow orders. Or you can operate in neutral space - everyone you see is a potential friend or enemy (more likely enemy). Or you can go deep into enemy space and play cat and mouse with an entire alliance for hours or days.
So... yes, I guess?
Also, "be alone" and "be a follower" aren't the only options, there's also plenty of room for leaders (well, plenty of opportunity for a leader to make room for themselves and their followers :P).