Flowing water and brine have been proposed to cause seasonally reappearing dark streaks called recurring slope lineae (RSL) on steep warm slopes on Mars, along with other formation mechanisms that do not involve water. This study aims to examine whether the evaporation of water vapor from the RSL, whether from fresh water or brine, is detectable by observing water vapor and/or clouds. In this study, we summarize the possible rate and duration of water-vapor emission from RSL in different scenarios, simulate how the emitted water vapor behaves in a global climate model, and discuss the detectability of water vapor in nadir observations during existing and future explorations. We found that, in typical cases, rapid horizontal dissipation within the planetary boundary layer (PBL) following the release of water vapor prohibits cloud formation and the excess water vapor from being distinguished from the background with existing observations. Thus, we conclude that the lack of correlation between the RSL activities and the overlying water-vapor column density does not necessarily rule out the wet origin of RSL. Nevertheless, we also found that water vapor tends to accumulate in basins and valleys in some cases due to the combined effects of topography and low PBL; we suggest the locations of such configuration as targets for future atmospheric studies of Mars dedicated to quantifying water-vapor release (associated with RSL) to elucidate the formation mechanism(s) of the RSL on the planet.