Not all the time. It depends on the fare, routing, time of year etc etc.
There are many economy class codes available for just 'economy'. So what you think you're getting may not be so.
For fares from Jakarta, the SQ website will show what's published. Most people would just book through travel agents who have access to special deals not available on the website. In Singapore however, rules permit special fares to be displayed on SQ's website which will be the same as you call a local travel agent.
So yes.. in a nutshell, what you ask for may not be available ..