Can I have an InnoDB master and MyISAM slaves with Full-Text for searching? I'd like to use InnoDB on the master, for its transactional ability, but MyISAM on the slaves for the full-text search ability. Is this possible?
Absolutely !!!
Just run ALTER TABLE tblname ENGINE=MyISAM; against all tables on the Slave that you want to have the FULLTEXT index. Afterwards, you can run ALTER TABLE tblname ADD FULLTEXT (column[,column]);.
Please be very careful not to run DDL against those tables in the Master that are unique to InnoDB that will replicate to the Slave.
I have suggested using a different Storage Engine on a Slave in my past posts:

Jun 01, 2011 : What can we do in MySQL 5.0 Replication to address bandwidth concerns?
Nov 16, 2011 : Log MySQL DB changing queries and users
Mar 13, 2012 : https://dba.stackexchange.com/questions/14943/setting-up-mysql-across-a-series-of-production-servers/14945#14945