Yes the left column would deflect in the real world. The reasons are:
1) Eccentricity of the connection / column:
In reality the load will not be transferred perfectly to the center of the column nor will the column be perfectly straight. This will cause a small amount of bending in the column. In most cases this will be extremely small. However, if the column is slender and the load is large this will cause buckling to occur significantly below the theoretical Euler buckling load. The variation in cross-section is accounted for in the building code material factors. Geometric imperfections must be explicitly checked. For example: Clause 5.2 in Eurocode 2.
2) The connection is not a true, friction-free hinge.
Here is a picture of a typical steel 'pinned' beam-column connection:
Clearly, this is not a friction free hinge and some bending will be transferred to the column. This bending transfer will be small assuming the deflections are small (which they typically are in structures). There is usually some play in the connection as well which will allow some movement. But the bending transfer will not be zero.
2) There is no such thing as a perfectly fixed support.
The foundation has some (non-infinite) stiffness, therefore the fixed support could rotate a small amount. An interesting exercise for the keen reader would be to consider a concentrated moment on an infinite half space made from sold steel (or another material) to get the foundation stiffness then see how this affects the deflection of a cantilever. But I digress...
Ultimately, as with many things in engineering these deflections are very small in typical design situations and are therefore not usually explicitly calculated/considered. However, they do exist. We should not forget the idealisations we make for calculation convenience are simplifications which could have real consequences if not understood.