Atmospheric Humidity Effects on Non-water Evaporation
Yes, because though the liquid phase initially contains no water, water molecules may enter the liquid phase from the gas phase.  The more hygroscopic the liquid is, the more the evaporation rate will be affected by humidity.  If the liquid is very hygroscopic and has a low vapor pressure, the initial evaporation rate may even be negative in humid conditions, as water enters the liquid phase at a rate greater than liquid enters the gas phase.