I think, first I should clarify what causes the osmotic pressure:
Osmosis occurs when two solutions of different concentrations are separated by a membrane which will selectively allow some species, e.g. the solvent, through it but not others, e.g. the solute.
So, there is a concentration gradient between the two solutions which would lead to a diffusion from the side with the higher to the side with the lower concentration.
But since the solute cannot pass through the membrane the diffusive flow cannot even the concentration differences out and thus constantly presses against the membrane exerting a force on it which leads to a pressure.
The pressure originating from this tendency for osmotic flow to occur is called the osmotic pressure $\Pi$ of the solution.
So, the question is: Is the theory behind diffusion applicable to colloidal solutions?
To reason about this, I will first address the matter of whether colloids can be considered "real" solutes or not. Colloidal particles are usually some polymer particle coated with a tenside layer. So, it is the molecules of those tenside layers that interact with the solvent molecules and they are chosen in such a way that the colloidal particles neither lump together (coalesce) nor sink to the ground or float to the top - that keeps the colloidal solution stable. So, a colloidal particle is surrounded by solvent molecules which solvate the tenside layer. Of course, the situation is a bit different from a "normal" solution since the colloidal particle is a lot bigger than, say, an alcohol molecule and thus the the ratio between solute particle size and the size of its solvation sphere is much smaller. But, in essence, a colloidal particle and an alcohol molecule are solvated in pretty much the same way.
Furthermore it can also be assumed that interactions (e.g. electrostatic forces) between the colloidal particles are weak.
This means that colloidal particles are thus not subject to external forces which influence their movement. They simply move through the solution by Brownian motion. This is important because then their motion can mathematically be described by a stochastic process which is the basis for the thermodynamic description of diffusion.
And, as I described above, the reason for diffusion to happen is the same as the origin of the osmotic pressure.
So, to answer your last question: Yes, I think, the description for osmotic pressure caused by colloidal particles should be the same as for "normal" solutes.
