Yes, schema changes replicate as any other event. MySQL slaves replicate master's binary logs into a relay log and then executes the events. Of course, this is if
replicate-do-db or another variable identifies the specific scope in question to execute the statements.
There was a bug in MySQL, where if you executed alterations by specifying the table as
database.table, it would not replicate. It required a
use statement to proceed the queries that matched a
replicate-do variable to actually execute the queries. I believe this is addressed in the current version but is still something to be aware of.
This functionality is well documented on the MySQL Web site.