My name is Michael, I’m a Guru here with Shopify, thanks for getting in touch. :)
The SEO or SERP would not be effected by changes to the Theme or by switching to a new theme as the SEO for a site is managed from the admin or backend of your site, the storefront's theme is a layout of how the content in the backend is portrayed to the customer, it doesn't effect the content directly. You can see a post that I made previously on the subject of SEO or SERP here.
I hope this helps and best of luck with your Business going forward! :)