No, not really.
Some of the essential oils are toxic to a variety of invertebrates, but they may then also be toxic to you/your pets (for example, lavender, peppermint, tea tree can all cause inhalant irritation and skin burns)...
Most of the spiders you see in your home have always been in your home, they were born there, as were their parents and so on.
This particularly applies to common house species: House spiders, noble false widows (the other two are more outdoor), cellar spiders, sac spiders, missing sector orb weavers and a fair few more.
You see more in autumn as thats typically breeding season and it means males lose their minds completely and risk coming out into the open to find a lady friend, fight with other males that cross their paths etc.
Occasionally an outdoor species will wander in, its accidental, the outdoor species do not want to be in a too warm, too dry house with insufficient prey.
Potentially, trying to remove spiders will mean you see more (as spiders move to fill empty territories), so its probably better to learn to live with them. They do provide a useful service in eating a lot of much less pleasant house-dwelling/house visiting species.
I currently employ a crew of pholcus (cellar spiders) around my frog vivs, to tidy up the escaped fruit flies, and my resident zygiellas (missing sector orb weavers) on the windows catch any annoying houseflies, moths or wasps that bash around the window frames.