Sephadex and purification of products
First, a conceptual but important point: there is nothing that sets artificial (a better word is synthetic) chemicals from natural products, chemically speaking. What we call "natural products" tend to be larger, complex molecules largely because we reserve the term for compounds for which extracting from natural sources is easier than synthesis, and these tend to be very large organic or bioorganic macromolecules, but there's no fundamental difference in behaviour between natural and synthetic molecules of those compounds, and in principle we could synthesise any natural product and reproduce exactly the same chemical properties that the same compounds have when extracted from natural sources. I state this because your use of the categories of natural and artificial can suggest some essentialist distinction while there is none.

Now, as to whether Sephadex can be used to separate and purify synthetic compounds, the short answer is yes, if these compounds are suitable. As @Waylander mentioned, and as with any separation medium, the main question is whether the compounds you want to separate are in the fractionation range of the medium. Sephadex can be manufactured with different bead sizes, which result in different separation ranges (these are marketed as G-10, G-25, ..., G-200). Different Sephadex gels can are used to separate proteins in the range from a few kDa to hundreds of kDa - and in principle they will be useful to separate synthetic organic compounds in the same molecular weight range through size exclusion. Commercial products are generally considered capable of discriminating molecules above ca. 700 Da.

Another factor to consider is functionalisation: Sephadex is highly functionalisable, which can produce specific affinities and retain desired compounds. This allows for a large range of possibilities for purification or separation, depending the composition of your mixture, what you want to retain and what you want to remove.

In practical terms, it is probably wise to begin by looking at separation procedures involving compounds of similar molecular weight and functional groups to those of your compounds of interest that are already described in the literature and work from there.