Yes it does!

Stored Procedures, Functions, Triggers and Views are all backed up by the SQLyog backup tool (and restored by the restore functionality). That applies to all connections types - also HTTP-tunneling.

You also have the option to deselect the backup any of the object types, if you like.

Also the partition structure of MySQL version 5.1 partitioned tables is backed up.

But please note that to backup Stored Procedures, Functions and Views the complete database must be backed up, not individual tables. Triggers however are defined as 'belonging to' a table and will be backed up with the table.