I'll take a different approach than the other answers: yes, it's likely you'll have issues switching to Shopify if you don't plan absolutely everything.

Now, if your site is making no money or a limited amount of money, the stakes aren't that high. But if you're making a substantial amount of money for your business from your ecommerce platform, then the stakes are absolutely high.

Here are the questions to ask:
-Do you have complicated, custom products that require configuration? If so, then really evaluate if the switch makes sense and can be done within scope.
-Do you have tons of product, over 1,000? If so, then take a good look at whether Shopify is the best.
-Are you using features on your legacy platform that are crucial and not built into Shopify?
-Are there certain traits on your site such as internal links or category page content that is difficult or different to implement on Shopify?
-The list goes on

Don't just flip the switch and hope it works. Shopify can be great for SEO, and better than your current platform. Or it can be way worse, depending on where you're coming from.

I don't care if you go to this link or not, just wanted to let you know I've thought about this a good amount and I'm continuously updating this page on all Shopify SEO topics - https://www.greenflagdigital.com/shopify-seo/