Yes, Teiid can automatically load the data into Mysql using the external materialization feature. Here is an external materialization example , which depends on the data-federation example  for its data. The materialization, in this example, is configured to reload the h2 table every 60 seconds, but that's configurable. Take a look at the portofolio-mat-vdb.xml as to how its configured. Full details on using external materialization can be found here .
Another option for automating the load, you could use cron job to submit the sql to perform the "select into".
Please reach out if you have any questions.
Thanks for your reply, Van Halbert.