Decoupling has nothing to do with the stability of the power supply. Decoupling is needed when a chip might change it's current draw rapidly. When this is the case, inductance in the wiring can cause a glitch in the power, whether it is a battery or a regulated or unregulated mains fed supply. Since a '555 can cause a rapid change in current as it's output switches, it *might* need decoupling. Whether it actually does or not need one for reliable operation would depend on the particulars of the design.
Good practice would be to always use decoupling. It can't hurt and it might help.
Bob