You could use phpMyAdmin or similar tool to change the table engine to one that does support FULLTEXT.
This post may or may not help:
My guess is the host is on an older version of MySQL and the default table type is InnoDB. IF, that is the case then you need to change the engine type for all the Connections tables in the DB to MyISAM.
If you decide to do this, backup the db first in case something goes wrong. And after you change the table engine, go to the Connections : Settings admin page and ensure the FULLTEXT option is enabled under the Search tab. Whether or not you have to change this settings you will have to click the SAve Changes button so the indexes are created.
Hope that helps.