In a vacuum chamber, the lack of atmospheric pressure does indeed affect the vapor pressure of liquid water. The vapor pressure of a liquid is the pressure exerted by its vapor in equilibrium with the liquid at a specific temperature.
The vapor pressure of water is influenced by temperature and the presence of other gases (such as air) in the surrounding environment. At a given temperature, water reaches its equilibrium vapor pressure when the rate of evaporation from the liquid surface equals the rate of condensation from the vapor.
In a vacuum chamber, where the pressure is significantly lower than atmospheric pressure, the vapor pressure of water will be lower than it would be at the same temperature in the presence of air. The actual vapor pressure of water in a vacuum chamber will depend on the specific temperature, but it will be lower than the vapor pressure at the same temperature in the presence of air.
The statement you've heard about water in a vacuum chamber reaching a vapor pressure of 17 mmHg is not accurate. At 20°C, under standard atmospheric conditions, the vapor pressure of water is around 17.5 mmHg. However, in a vacuum chamber, where the pressure is significantly lower, the vapor pressure of water will be even lower.
In summary, the lack of atmospheric pressure in a vacuum chamber does affect the vapor pressure of liquid water, and it will be lower than the vapor pressure at the same temperature in the presence of air. The exact vapor pressure in a vacuum chamber will depend on the specific temperature and the degree of vacuum present.