The answer to your question is no.

There is no such thing as 'tabids for the menu'.  The menu is a derivative of the Tabs table generated dynamically at runtime for each page, it doesn't exist as a separate entity.  I think you should look at other ways of achieving your outcome and forget about the menu.

The Desktop Tabs collection shoudl be cached, but you will need to check your database access by using a query analyzer tool to sniff the database traffic to your database to know for sure.  I think the code above will run without accessing the database.  My other suggestion is concentrate on overall page performance and not to worry too much about database access unless you are repackaging the module for use by other people when you don't have control over the number of tabs and traffic to their site.  If  you've got 10 tabs in your portal, it's not really going to matter much if you request that twice.  You can always build your desired tabs collection and cache it yourself so you know exactly when and why a query will be run. 

//Build list of tabs to be shown to user