By temporarily dropping secondary indexes from the new table before copying the data, and then recreating them later, ALTER TABLE can take advantage of the fast index creation feature even when it has to copy the entire table.
In most cases, InnoDB is the correct choice for a Drupal site. It provides increased concurrency, enhanced performance and much more data integrity than MyISAM ever can. However, the pluggable nature of MySQL engines allows the user to "mix and match" table engines inside a single database. This allows us to consider tables whose workloads fit MyISAM more so than InnoDB. The main candidates for MyISAM in a mostly InnoDB-centric database are the search tables.
