My hunch is yes, but I can't think how to prove it. An argument against this is you have a box with a divider in the middle, one side is filled up higher than the other. The divider is removed, you will get waves in the fluid, when the viscosity is lower the waves will continue for longer, so when the viscosity is zero nothing will stop the waves so they will never stop, ignoring friction with the sides of the box. Is this right?
Viscosity is the only dissipating mechanism in a fluid absent outside forces (gravity, magnetic/electric fields if the fluid responds to those, etc.). So if there are no outside forces, it will continue moving forever.
Of course, this is only academic because a truly zero-viscosity fluid doesn't exist (well -- superfluid helium is a thing, but it would require constant energy removal for it to stay in that state, otherwise perpetual motion would be possible).
But, this all hinges on how you define "equilibrium". For example, would a stationary vortex be in equilibrium? It would be time-invariant, so I would call that an equilibrium but maybe you don't. It's hard to say without being more precise. However, it is possible to find many time-invariant solutions to the Euler equations (ie. the equations that govern a fluid when viscosity is neglected) so it boils down to definitions.