Can single sign-on integration be used even if an invalid email address is registered as the Salesforce username?

Yes, it is possible.
If an invalid email address is registered as the Salesforce username, please set up single sign-on between Salesforce and the Teachme Series using an integrated ID.

Related: How to choose the subject type and what to watch out for when setting up single sign-on with Salesforce
https://help.series.teachme.jp/hc/en-us/articles/63062071147289

If you are unable to link single sign-on using an integrated ID and need to set up single sign-on with the Teachme Series using an invalid email address, please contact us in advance via the Contact form with the following information.
We will confirm whether any alternative solutions are available and whether there is any impact on the Teachme Series service as a whole.

• Group number
• Number of invalid email addresses you wish to register
• Background on why invalid email addresses need to be registered
  Example: An invalid email address is registered as the Salesforce username.
  It cannot be changed to a valid email address due to operational reasons in Salesforce.
  Additionally, single sign-on linking 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