You can still look for He'Stan and the Artefacts if you choose a non-Forgefather option, but at the same time choosing Tor'Kell doesn't mean you'd be somehow exempt from your duty to defend the Imperium, far from it. Would Vulkan be happy to know his sons ignored the people they were sworn to protect in favor of trying to find him?
It's more about the level of focus, and how much it influences your Chapter culture. Ko'Tan will push you towards being great fighters and honourable protectors of the common man, N'Varr will influence you towards diplomacy, naval warfare and organization, while Shal'Dar's deal is being aggressive hunters of the Imperium's many enemies. Tor'Kell will push you towards being artefact-seekers and tech/craftsmanship oriented (he was a Techmarine before becoming Forgefather, after all), but even then the Quest for Vulkan will not be the totality of your Chapter.