Yes and no, I'd expect efficiency to change, but not the pump curve - depends on what you mean by negative suction head. I'm not sure if you mean you plan on running the pump is a suction lift condition, or just operating at a lower-than-rated suction pressure.
Basically, if I assume you're talking about operating a centrifugal pump under a suction lift condition (that is, liquid level is below pump suction) the manufacturer's curve shouldn't change. I say shouldn't, because every manufacturer's curve I've seen describes flow vs. total developed head. It's a differential pressure curve that is only changed by changing pump speed or impeller geometry.
However, if you run a pump at a lower suction pressure and the same discharge pressure, it will increase the differential pressure (total developed head) that the pump sees, it will probably change the location of the operating point on the pump curve, and result in a reduced flowrate. Centrifugal pumps are head-hunters, they'll go to the point on the curve which matches the differential pressure they see, and deliver the flow corresponding to that point. As the operating point moves around on the curve, efficiency does change. It's impossible to predict without knowing the curve, but it should be easy to read off the manufacturer's pump curve once you know what you're looking for.
Sorry, I know that's a little vague, but if you can give me a little more detail I might be able to tighten that up a bit.