satsuma, I'm no rulemaker or anything, but I'd vote on "you need to use the sine sample provided." If you understand additive synthesis with using a sine as the source, there should be nothing holding you back to reproduce this manually via samplers. I'm using this method as well for some of my sounds and there is definitely a charming quality to the slight imperfections in my squares and saws produced manually through use of the overtone series. Even more of a charm when you start adding them; you would definitely hear a difference between building them yourself and what would be built perfectly by an additive synth like the one you describe. Not even mentioning the great saw you'd get by setting the loop point at quarter cycle or getting a square-like one from crushing the waveform with different types of distortion...could take it even further by playing with phase relationships, detuning, etc. (like null1024 said!)
Even if there were samplers that provided an overtone/additive feature, it would still sound quite different since you have to manually set loop points. I've never heard of a sampler that provided this function, but kudos if you make your own Max/MSP patch or get jiggy with python or something.
For these reasons, I feel, a sine isn't a sine isn't a sine and it's the beauty of this compo: breaking down sampling and synthesis to its core and seeing what people do with it.