MyDomain is a pre-requisite for SP Initiated SSO, where Salesforce is the SP.
Even if MyDomain has not been rolled out to Users, it is available to System Admins to test in the intermediate state. You can try to authenticate into salesforce by referring to your MyDomain Link, at the top level as well as a deep link to a resource. In the latter case, the resource URL is passed as the RelayState in the SAML, so that the User lands straight onto the resource url.
You might want to completely roll out MyDomain on a (preferably Full) Sandbox so that users around the world can test it.
Old (Pre My Domain Links) can redirect to the new URL (with Warning, if needed), so that does relieve some of the testing pressures, but it would be wise to test some deep links that users may have bookmarked or have been embedded in external systems.
If you intend to turn off login from login.salesforce.com at a later point, it might be wise to get people to start updating Chatter Mobile / Desktop to point to the My Domain URL.
Here is a previous response, which might help. And another.