Not personally, but I've barely been on the shot for a few weeks now. Still, nausea has not been one of my symptoms. I was getting night-time nausea on occasion when I was on the pill but it wasn't regular so I don't think it was related.
However, many women do experience nausea on hormonal birth control so it's entirely possible. She should call her gynecologist and ask if this is a symptom of the shot. Otherwise, why not consider that she's actually sick?