To be perfectly honest, no one needs a "system" to rp. When I was five and playing "Army men" We didn't have a "system" and somehow it was pretty fun. Lots of cheating, but still fun.
As for rolling up a character and putting all the stats on a piece of paper that too is not "necessary" either, but it does quantify your character's abilities.
So no, one does not "need" a system or a character sheet, BUT, if you want to be fair to everyone including the monsters you will need a system with rules and a character sheet with abilities to play fair for everyone, or else you will hear the same old, "I got you. No you didn't. Yes I did! No you didn't." that we all got sick of when we were seven.