Yes, they do apply market pressure. They can change who they buy from and there are different deals - like fixed rate, or different charges for different time periods.

The intermediate players "electricity retailers" then participate in a day ahead and real time market to fulfill their obligations to their customers.

You'll find most markets actually work this way. When I go to the supermarket to buy sugar, the price isn't jumping around real time with the underlying price of sugar. Same for coffee etc. But it changes with a lag, and consumers respond and the effects flow through even if not in real time.