What you're talking about here is the concept of compatibility (which I hope you've already encountered if you're in a structural program). oil field trash's answer touches on this, in a nontechnical way.
Materials deform not just based on their material properties, but also the geometry of the materials as well. In structural engineering, we like the term "stiffness" for this. You've probably already encountered this idea when calculating things like beam deflection or axial strain - the deformation is based on only on the elastic modulus, but also things like the length of the member, its area, its moment of inertia, etc. For different modes of deformation, different properties are needed (for example, for axial deformation the length and area are used, while a beam in bending the length and moment of inertia factor in).
When materials restrain one another, their deformations have to be compatible - that is, the interface for the two materials will move the same amount for each as a result of their strains. This provides us an additional equation for analysis, meaning we can solve for additional variables (very handy).
Your scenario is a complex one, but the simple answer is that yes the steel will deform some. Enough to matter? That's an undefined concept, how much is enough to matter, it would depend greatly on the application. In building construction, you can be off by a pretty noticeable bit and still make things fit. In the inner workings of a clock, if things are off a little bit you get a bad clock.