  Recent observations have demonstrated that some subset of even moderately
wide-separation planet-hosting binaries are preferentially configured such that
planetary and binary orbits appear to lie within the same plane. In this work,
we explore dissipation during the protoplanetary disk phase, induced by disk
warping as the system is forced into nodal recession by an inclined binary
companion as a possible avenue of achieving orbit-orbit alignment. We
analytically model the coupled evolution of the disk angular momentum vector
and stellar spin vector under the influence of a distant binary companion. We
find that a population of systems with random initial orientations can appear
detectably more aligned after undergoing dissipative precession, and that this
process can simultaneously produce an obliquity distribution that is consistent
with observations. While dissipative precession proceeds efficiently in close
binaries, favorable system properties (e.g., $r_{out} \gtrsim 100$ AU, $\alpha
\gtrsim 0.05$, and/or $M_b/M_{*} \gtrsim 1$) are required to reproduce observed
alignment trends at wider binary separations $a_\mathrm{b} \gtrsim450$ AU. Our
framework further predicts that circum-primary planets in systems with high
stellar mass ratios should be preferentially less aligned than planets in
equal-mass stellar binary systems. We discover tentative evidence for this
trend in \textit{Gaia} DR3 and TESS data. Our findings suggest that dissipative
precession may play a significant role in sculpting orbital configurations in a
sub-set of moderately-wide planet-hosting binaries, but is likely not solely
responsible for their observed population-level alignment.
