Can single sign-on integration be used even if an invalid E-Mail Address is registered as the Salesforce username?

Yes, it is possible.
If an invalid E-Mail Address is registered as the Salesforce username, please configure Single Sign-On between Salesforce and the Teachme Series using an integrated ID.

Related: How to choose the subject type and what to keep in mind when setting up Single Sign-On with Salesforce
https://help.series.teachme.jp/hc/en-us/articles/63062071147289

If Single Sign-On integration using an integrated ID is not possible and you need to set up Single Sign-On integration with the Teachme Series using an invalid E-Mail Address, please contact us in advance via the Contact form with the following information.
We will check for alternative solutions and whether there is any service impact on the Teachme Series as a whole.

• Group number
• Number of invalid E-Mail Addresses you wish to register
• Background on why invalid E-Mail Addresses must be registered
  Example: Invalid E-Mail Addresses are registered as Salesforce usernames.
  They cannot be changed to valid E-Mail Addresses due to Salesforce operational reasons.
  Additionally, Single Sign-On integration using an integrated ID is not possible due to constraints with other services.

Related: Single Sign-On Setup with Salesforce (Web Browser)
https://teachme.jp/8/manuals/51167358