Does time pass at all for a system at equilibrium

A system in perfect equilibrium is not perfectly stationary in space or time. But, any change in the system is offset by another change such that there is no net change.

Let's look at a simple example. Take a perfectly insulated box isolated from the environment and fill it with a gas. The gas molecules are all bouncing around, hitting each other and the walls, and in general are very dynamic. However, if there are no temperature gradients, no chemical changes, etc then the system is in equilibrium.

It doesn't mean things aren't moving and events aren't happening: it means the events that do happen do not alter the state of the system, however you choose to define the "state." Usually a statistical description is taken to define a "state", although in some cases it is much simpler to take a macroscopic description like a motionless ball sitting in a hole.

As long as matter is present or in a definition of a system is involved (i.e. space between distant matter), time will be present and go on.

This because of every atom, even every single Fermion and every Boson is constantly changing, either via its virtual quantum activity due to movement or due to the ongoing elementary physical interactions.

For a Boson time flows always due to mere fact that it is propagating through space and thus changing its probability for reacting with a Fermion.

But as long we do not know exactly, what time is in its essence, we can not answer the question in full.

So the solely fact of the existence of matter in space, even in the distant space, let's time be present. Your question touches the issue of the mechanism of "existence" itself and this is not properly defined in physics.