Will any alkaloid dissolve in naptha leaving impurities to settle and be removed?

No, depends on alkaloid, you have to look up the solubility of each specific alkaloid in the different solvents.. For example, mescaline would not dissolve in naphtha, neither would any of the harmalas, neither would bufotenine, neither would DMT N-Oxide (though DMT N-Oxide does dissolve in naphtha if naphtha has some oils in it). Maybe 5-MeO-DMT would but its unsure at this point. So you'll have to be more specific.

Most alkaloids have certain solvents they react best with.
It's best to research the solvents for each different alkaloid your curious about independently.

If your wondering about just DMT, then Naptha works but it does pick up some DMT-like alkaloids as well. There are others available that will work better to specifically pick out DMT crystals.

Where would I find information on the solubility of different types of alkaloids in different solvents? Or is there a formula or some other math to figure it out?

The Nexus WIKI is a good place to start. There is no general rule... Although there are some guidelines (polar substances tend to dissolve in more polar solvents, less polar solvents in non-polar solvents), there are many exceptions, so in the end only practice will tell.

Thanks