You will not be overloading your main panel, your main panel would draw only as much as your main breaker can handle.
If your main panel is full and you add another subpanel, as long as you don't go over the rateing of the main breaker you are fine. You could have a full main panel as well as 10 subpanels that are all full but as long as you don't exceed the main breaker you will have no problems.
When adding a subpanel, does the load for the MAIN panel become the sum of the loads of both panels or is it calculated differently?
What if additional subpanels are added?
You are correct. If you are doing a load calculation for your service, you would add the service panel (main) loads plus the sub panel loads from all sub panels. Note, we are talking about actual loads and not merely adding up the sums of all branch over current devises.