On triggers and replication in MySQL
Yes, you are correct. You can often get bitten from the fact that the triggers are missing on the slave and thus the trigger effects are not there.

Also if the triggers use any routines (PROCEDUREs and FUNCTIONs) you have to make sure they are present on the slave too. The latter might bite you if you provision your slaves from a mysqldump, since by default mysqldump does not dump routines.