Sorta. The electrolytics are the reserve tanks, and hold the supply from power fluctuations, etc...

I will give you an example of how important those filters are. Well lets say that you have switching currents going on between logic ICs, it causes power fluctuations on the supply line. If the fluctuation is "great" enough, it drops the outputs of the logic ICs which will cause the demand to lower, and raise the supply voltage again. Then once that happens, it sags again.. This is called a parasitic oscillation. This could happen if the filters got bad enough. Where the noise gets into its inputs/outputs and affects the over all operation.

low-value decoupling capacitors are designed to stop parasitic oscillations in the high frequencies. The high value electrolytics are required to stop parasitic oscillations in the lower frequencies.

The small value ceramic capacitors that are in parallel, are the decoupling bypass caps.