  Correlations in and with the flux transmission of the Lyman$-\alpha$
(Ly$\alpha$) forest in the spectra of high-redshift quasars are powerful
cosmological tools, yet these measurements can be compromised if the intrinsic
quasar continuum is significantly uncertain. One particularly problematic case
is broad absorption line (BAL) quasars, which exhibit blueshifted absorption
associated with many spectral features that are consistent with outflows of up
to $\sim0.1c$. As these absorption features can both fall in the forest region
and be difficult to distinguish from Ly$\alpha$ absorption, cosmological
analyses eliminate the 12 - 16% of quasars that exhibit BALs. In this paper we
explore an alternate approach that includes BALs in the Ly$\alpha$ auto
correlation function, with the exception of the expected locations of the BAL
absorption troughs. This procedure returns over 95% of the pathlength that is
lost by the exclusion of BALs, as well as increases the density of sightlines.
We show that including BAL quasars reduces the fractional uncertainty in the
covariance matrix and correlation function and does not significantly change
the shape of the correlation function relative to analyses that exclude BAL
quasars. We also evaluate different definitions of BALs, masking strategies,
and potential differences in the quasar continuum in the forest region for BALs
with different amounts of absorption.
