  Despite a burgeoning set of ultracool dwarf ($\leq$M7) radio detections,
their radio emissions remain enigmatic. Open questions include the plasma
source and acceleration mechanisms for the non-auroral "quiescent" component of
these objects' radio emissions, which can trace Jovian synchrotron radiation
belt analogs. Ultracool dwarf binary systems can provide test beds for
examining the underlying physics for these plasma processes. We extend a
recently developed occurrence rate calculation framework to compare the
quiescent radio occurrence rate of binary systems to single objects. This
generalized and semi-analytical framework can be applied to any set of
astrophysical objects conceptualized as unresolved binary systems with
approximately steady-state emission or absorption. We combine data available in
the literature to create samples of 179 single ultracool dwarfs (82 M dwarfs,
74 L dwarfs, and 23 T/Y dwarfs) and 27 binary ultracool dwarf systems. Using
these samples, we show that quiescent radio emissions occur in $54^{+11}_{-11}$
- $65^{+11}_{-12}$ per cent of binaries where both components are ultracool
dwarfs, depending on priors. We also show that binarity enhances the ultracool
dwarf quiescent radio occurrence rate relative to their single counterparts.
Finally, we discuss potential implications for the underlying drivers of
ultracool dwarf quiescent radio emissions, including possible plasma sources.
