Does the information in the way-back archive really change the value of the domain? For example, a domain (un-reged) was reged in 2001-2004, would this increase the value?

The fact that it is/isn't in the wayback machine has no bearing on it's value.

The only value is seeing what the name has been previously been used for.

ok, just thought it would have some traffic coming to it depending on how big it was