Yes, the schema manager (via the plugin manager) will execute all your DB upgrade scripts in order, assuming they are present in your deployed plugin. The naming convention for the folder structure in your plugin folrder is ../src/database/upgrade/n/ where n is the version number(s), beginning with 1. In each of these folders, your DB upgrade script must match the following pattern:
{plugin}_{dbtype}.sql
where {plugin} is the schema name for your plugin (from the <databaseKey/> element in your plugin.xml), and {dbtype} matches the target database type (e.g. "mysql").