SEO mainly focuses on the acquisition part of the funnel: making your shop appear more often in Google and to a lesser degree getting searchers to your shop. As for converting them to buy, that's typically further down the funnel (having better landing pages, calls to action, navigation etc.).
That said, if the 'wrong kind' of users are coming to your shop via Google, SEO can be refined to help. For example, if you are appearing for searches related to [umbrella] but don't sell any, removing that keyword could help you perform better for things you actually do sell. However this scenario is quite rare.
So SEO helps you get more visitors to your shop, it doesn't help to convert them into buyers.
Worth considering also is that most shops convert only a single digit percentage of visitors into buyers. So having enough visitors to reach statistical significance is the first step which SEO helps with.