Does omitting the first two lines of RC4's pseudo-random generation algorithm weaken the cipher?
Yes, that omission weakens the cipher: the output  $\mathtt K$ has a short cycle (at most 65280 bytes) for a sizable class of keys (one in 65536). The following details why.

Because earlier code leaves $\mathtt i=256$ and the first execution of i := (i + 1) mod 256 makes that equivalent to $\mathtt i=0$, not initializing $\mathtt i$ makes no difference in subsequent code; and hence has no security implication whatsoever. 

But earlier code leaves $\mathtt j$ to a key-dependent value, thus the lack of initialization of $\mathtt j$ has an effect. In particular, if at the end of key scheduling $\mathtt j=1$ and $\mathtt S[1]=1$, then (by induction) during the whole of the stream generation we have $\mathtt j=(\mathtt i+1)\bmod 256$ and $\mathtt S[\mathtt j]=1$; thus the output generated has a short cycle of (at most) $256\cdot 255$ bytes.
This never occurs in real RC4 (as observed in 1994 by Hal Finney, in An RC4 cycle that can't happen, summarized on the RC4 page), but occurs for $2^{-16}$ of the keys in the modified cipher.