For many years after the adoption of RC4, it was known that there were pronounced biases early in the RC4 keystream. IIRC, these were the weaknesses that the 802.11 attacks too advantage of.
But the more recent TLS attacks are based on a better understanding of RC4 keystream biases, and some of them (the Fluhrer-McGrew biases, at least) persist throughout the entire keystream. I don't think you can simply encrypt a long nonce to avoid them.
(I'm not an expert on this and could be wrong, of course).