  Periodic signatures in time-domain observations of quasars have been used to
search for binary supermassive black holes. These searches, across existing
time-domain surveys, have produced several hundred candidates. The general
stochastic variability of quasars, however, can masquerade as a false-positive
periodic signal, especially when monitoring cadence and duration are limited.
In this work, we predict the detectability of binary supermassive black holes
in the upcoming Rubin Observatory Legacy Survey of Space and Time (LSST). We
apply computationally inexpensive sinusoidal curve fits to millions of
simulated LSST Deep Drilling Field light curves of both single, isolated
quasars and binary quasars. Period and phase of simulated binary signals can
generally be disentangled from quasar variability. Binary amplitude is
overestimated and poorly recovered for two-thirds of potential binaries due to
quasar accretion variability. Quasars with strong intrinsic variability can
obscure a binary signal too much for recovery. We also find that the most
luminous quasars mimic current binary candidate light curves and their
properties: false positive rates are 60\% for these quasars. The reliable
recovery of binary period and phase for a wide range of input binary LSST light
curves is promising for multi-messenger characterization of binary supermassive
black holes. However, pure electromagnetic detections of binaries using
photometric periodicity with amplitude greater than 0.1 magnitude will result
in samples that are overwhelmed by false positives. This paper represents an
important and computationally inexpensive way forward for understanding the
true and false positive rates for binary candidates identified by Rubin.
