How much difference does the placement of the shelf in the oven make to the final outcome of a cake?

Yes, it makes a difference. In a conventional oven (even one with a convectiono fan), anything placed on the bottom rack is going to absorb less radiation heat from the oven element. That means longer cooking times and possibly the need for a higher temperature setting.

If you're following a recipe then it's best to use whichever rack the recipe says. If the recipe doesn't specify, it's usually designed for the center rack.

Now, using a different rack is completely different from actually baking one thing on top of another thing, on a higher rack. That will have a significant effect on whatever is underneath, and if it is particularly sensitive to the time and temperature (many baked goods are) then it is very likely to fail entirely. I once tried to bake two layers of cream puffs and the ones on the bottom were still practically raw by the time the top was done. I doubt you'd find much better success with cakes.

A convection fan may help in this case, but I still don't think it's enough to compensate for the temperature gradient you'd create by "eclipsing" one dish underneath another in the same oven. You are literally blocking the heat from reaching the bottom dish.