Should I be worried about overwriting buildings?

When I place a new road or a building in a section I had previously zoned for RCI space, sometimes the new structure overlaps an existing RCI building. Simcity seems pretty relaxed about this, only highlighting the structure in yellow as I place the new structure, but not warning me excessively. When I finalize the placement of this new road or building, the RCI buildings that are highlighted are destroyed.

This usually fixes itself, a new RCI building is built in the reduced space now available. But should I avoid this? Does it cause any, to borrow a DF term, unhappy thoughts in my Sims?

No - I wouldn't be worried about overwriting buildings. From the beta testing I did I didn't notice any negative effects from destroying properties while placing new structures.

You are right that overlapping a structure over an RCI zone will not dezone that area - meaning that any buildings destroyed will free up the remainder of the space to allow new RCI buildings to be built in the smaller space that is left.

Destroying the RCI building would have removed the home or job for whichever Sims live or work there, but the employment model in SimCity is that agents simply travel around until they find a workplace requiring the type of agent they are (ie: high wealth).

In the event that any unhappiness is generated by the placement of the new structure, this would be counteracted by the happiness generated from placing the new structure.

For example, you will generate happiness in the region by placing schools, parks, police or fire stations in a residential area, placing casinos or other commercial buildings in commercial sectors, or placing large industrial buildings (including power plants) in industrial zones.