Nick here from Shopify. Great question!
It can take up to 48 hours for a domain to change over, but it rarely takes that long and can take only a few minutes sometimes. My advice would be to assign your .myshopify.com URL as your primary domain until you see the new domain all cleared and then assign the GoDaddy domain as your primary domain. Hopefully, it won't take more than a few minutes and minimal downtime for you, if any. Shopify has an in-depth help guide which you can read here, going into detail about all of this and more.
I hope that answers your question, but don't hesitate to ask if you have any others.