It depends on the microstructural/metallurgical condition of the stainless steel. If you are testing type 316L SS in annealed condition, probably you may not see any effect. Recall that implementing hydrogen chemistry is one of the ways to control corrosion in BWR. If you are testing weld or cold worked 304L, probably hydrogen may increase the susceptibility to SCC due to delta ferrite in welds or epsilon martensite or high dislocation density in cold worked materials.
Still the effect of hydrogen will be masked by dissolved oxygen (D.O) in the water, if D.O level is 0.2 ppm. Diffusivity of hydrogen is low and solubility is high in austenite to affect the mechanical properties. In short, the kinetics of hydrogen evolution is too slow to significantly affect the SCC or tensile properties of annealed austenitic SS. If at all there is an effect by hydrogen due to cathodic reaction or electrolysis, it will be positive - leading to decrease in SCC.