Can ordinary humans supply new Space Marine gene-seed?

Could a normal human with desirable qualities become the source of a new gene-seed line in Warhammer 40,000?

No. Gene-seed is tied to the Primarchs, while the Traitor Legions face separate problems replenishing losses.

Gene-seed belongs to the Primarch lineage and cannot simply be extracted from a promising ordinary human. The Emperor's use of the Warp in creating the Primarchs prompts disagreement over how directly to describe gene-seed itself as containing the Warp. A further contribution attributes the Traitor Legions' replenishment problems partly to damage from prolonged Warp exposure. Theft and other disturbing fictional methods are mentioned as ways those forces replace losses. These are interpretations of the setting's biology.