it is possible;
However, the reason why players opt to be part of PvP or pirate corps is for the social, economical and support aspects.
Social; if your new to pirating, having a corp help you out with builds, strategies and locations of populated tunnels in null and low-sec can really make you enjoy the process more. As well, it won't seem so lonely when playing an mmo.
Economical; Some PvP corps (especially the rich ones) help you out with ships and components, including reimbursement for ships you lose. There is also usually joint PvE operations to fund the expensive pirating hobby.
Support; If you get into trouble, you call upon corp or alliance mates to help you out. There is also a lot of fun in small-gang pirating if you wish to dip into that.