[WooCommerce] Will migrating Wordpress hosts disrupt my service?

Changing hosting providers is not ultimately disruptive to the integration, but does depend on your site's ability to be found online after making the switch.

When you switch hosting providers, your DNS (domain name service) will have to be pointed at your new host.  This means your site will be temporarily unavailable until the DNS servers are back online and your updated DNS server settings are propagated.

In most cases, this should propagate quickly (pro tip: the better the DNS and hosting provider, the faster this goes). However, your site will experience site downtime while DNS names are being propagated, so it's a good idea to enquire with your new hosting provider how much downtime to expect.

More info on what affects DNS propagation time (from GoDaddy):