Can I interpolate rainfall data from stations outside of watershed for the watershed?
Yes, you can interpolate the rainfall from stations outside the watershed. However, the quality of the interpolation will depend on the distance between the stations and the watershed, the prevailing weather patterns, and to some extent the topography.

For example, it probably wouldn't be appropriate to use a station on the rainy side of a mountain divide in estimating rainfall in the rainshadow. One way to get an idea on how good you estimates are is to compare the actual rainfall at a station with the interpolated rainfall at that location, when you leave it out of the dataset.