Order by varchar mysql
Nope. If you order by a not indexed column then the server HAS to load all the results into memory and can only then start sorting them. That is heavy - not sure how mySql does it, but on SqlServer that will also tax the tempdb for the temporary holding of the data. If it is a lot of data that may be super slow due to memory flowing over onto the hard disc.

Physics and logic can not be cheated, sadly.