As for your first question "is the S-box indistinguishable from a random permutation?", well, there are likely some subtle biases. For one, we know that, after exactly 4096 steps, the combination $j=1$ and $SBox = 1$ is impossible; that's because $i=0$ after 4096 steps, and the combination $j=i+1$ and $SBox[j]=1$ is known to be impossible (given the standard RC4 key setup; this was first observed by Hal Finney). Because of this, there is likely a bias away from $SBox = 1$ after exactly 4096 steps, and so this would appear likely to be a distinguisher (albeit not a strong one) from a random permutation.
As for your second question "are the bytes generated indistinguishable from random data?", the answer for that is "definitely not". We know how to distinguish a roughly Gigabyte output of RC4 from a random stream; see this paper for the details; note that discarding an arbitrary amount of RC4 keystream before you start sampling does not affect this attack.