Is the "SELECT field_names INTO OUTFILE 'file_path'" MySQL command supported?

The SELECT ... INTO OUTFILE ... function (to export a ".CSV" table for example) isn't available.

The "mysql.domain.xyz" SQL server is different to your FTP hosting and so the file wouldn't be created in the right place using this function. You can create a script however, to perform your export using a basic SELECT and then write the data via fopen() to a .csv file on your hosting. You can also make this export straight from phpMyAdmin.