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With these assumptions, we find an extinction due to gas in the Galactic disk (excluding Sgr B2) of $11\pm4~\rm{mag}$. In linear units, this corresponds to extinction by a factor of $\sim25,000$! Note that this value is very sensitive to the parameters adopted for the dense H$_2$ phase - a factor of 4 higher filling density or filling factor (i.e. 1 big cloud) would nearly double the total extinction.  Along those lines, when we add in Sgr B2, things get much worse for optical observers. As a rough estimate for the parameters from the cloud, most students adopted $D=45~\rm{pc}$ and $n=3000~\rm{cm^{-3}}$ e.g. \cite{Goldsmith}. If we assign a $20\%$ error to these parameters, this corresponds to $A_v=250\pm80~\rm{mag}$, or a visual extinction of order a factor of $10^100$ (i.e. opaque). I've used Monte Carlo simulations to propagate the uncertainties in these inputs and illustrate these distributions in Figure 1.