Broadband all-sky searches for continuous gravitational waves (CW) from isolated neutron stars typically yield a number of significant candidates that are discarded through hierarchical semicoherent and coherent follow-up searches. However, these searches target purely isolated sources and do not take into account possible phase modulations to the signals due to companion objects in binary orbits. If the source object is in a binary orbit, the signal-to-noise ratio (SNR) of a signal will diminish due to the mismatch between the signal waveform and the template waveform used in the search. In this paper, we investigate the sensitivity of CW searches to signals from sources in binary systems over an exhaustive range of binary orbits. We use Monte Carlo simulations to constrain the ranges of binary orbital parameters that leave a CW signal from a source in a binary orbit visible in a search for signals from an isolated source (isolated searches), and consequently tighten the parameter space explorable with dedicated searches for signals from sources in binary systems (binary searches).