Is it possible for the remaining solute of a saturated solution to form a single even phase from top to bottom (similar to that of a colloid)?
The density of the solute relative to that of the solvent will primarily determine whether the excess solute will float, sink or tend to disperse throughout the solution.  Additionally, the particle size and porosity will play a role in the rate of settling or floating, as will the viscosity of the solvent, but it is the density that determines whether the particles will float or sink.

But, the answer to your question is no. Even if the density of the undissolved solute is essentially the same as that of the solvent, and the undissolved solute is very fine, then you could have a uniform looking solution, but it would still be a two-phase solution, with a solid phase suspended in a liquid phase.