Will an ALTER TABLE ADD COLUMN on a slave break replication?
I think that, if your purpose is to avoid locking, you should use pt-online-schema-change (a tool from Percona Toolkit) or Gh-ost (from GitHub).

Here is how pt-osc works:


Creates a ghost table identical to the original table, but empty
Runs ALTER TABLE on the ghost table
Creates triggers on the original table, which insert new rows in the new table, and updates and deletes them if they are already there.
It copies the rows in chunks, monitoring the server performance (it can slow down or pause its work if necessary)
Switch the table names


gh-ost is very similar, the main difference is that it creates no triggers, and uses the binary log instead to detect the changes to the original table.

To answer your question more directly - yes, it is possible to add a column on the slave. And most probably it will simply work, as long as it has a default value. But it is very likely that in the future you will regret this choice, because you'll need to do something that will break replication, like adding a column in the master. I recommend to sure to check the documentation and fully understand the dangers, before doing such a thing.