No, you can't.

An index, in MySQL, will either be 

- a `BTREE` single or multi-column index.

- a `HASH` index (available only for `MEMORY` tables), that can span several columns.

- a `SPATIAL` index (available only for `MyISAM` tables).

- a `FULLTEXT` index (available for `MyISAM` and 5.6.4+ `InnoDB` tables), that can span several columns of `CHAR`, `VARCHAR` or `TEXT` type.

You can't combine these types.

[1]: https://dev.mysql.com/doc/refman/5.6/en/fulltext-search.html