Yes, we support the tsearch2 module for PostgreSQL. Please check if this module has already been installed on your database. If not, you can open a support ticket with our Guru Crew at http://my.a2hosting.com and we will enable it for you. Please include the full database name in your ticket.
For more information about the tsearch2 PostgreSQL module, please visit http://www.postgresql.org/docs/9.2/static/tsearch2.html.