The anarchisitc idea that we don't need rules is very highly based on a complete social revolution and says itself that it is based on us living in a way that we are led to believe by the government/brainwashed that it won't work.
Therefore by definition the only way to find out if it would work is to try it. This perfect for the idea as it increases the likelyhood of this ideal being tried to be reached.
I personally think that anarchism is just an ideal, IMO humans are egoistic, if I can get away with something then I will do it if I want to, its the fear of the consequences that stops us.
I'm not so sure about egoism playing any different a role as it does already. I had a bit of trouble reading your post, so I'm not sure if I've mis-read some of it, though. In the long run, we'll probably just end-up back where we started. A channel 4 documentary left about 10-12 kids in a small village without guidance or rules for a time, and they were observed without interference. After the big egos were satiated, everyone settled down into some kind of role within the village, it wasn't long before a "structure" emerged and the kids began creating their own society, complete with formal rules!
Anyway, the important points are that not everyone responds in such a way as I interpret you to have meant (as in, not everyone acts in a direct, self-serving manner, thanks admittedly to socialisation in part, I would suggest). But also, it highlights the progressive nature of law, and if that experiment were to be repeated, the same outcome would surely be observed, demonstrating this point. If you wish to see this in action, merely go and talk to someone or observe an interaction!
Repression or some kind of personal imbalance sounds like as much of a cause of any form of "raw behaviour" as anything else would be. For many people however, they realise the functions and thereby the necessity of rules and are happy to exist within them. Laws are merely extensions of norms and values anyway. So, they would continue to exist for as long as social animals do in some form or other.
So I would say no, it's not possible on the basis that even if you remove the word "law" its function would remain in some form.
EDIT: Clarification and elaboration
EDIT 2: Correction