Is my simple atmega2560 based product exempt from EMC testing?
You should define which market.  

For the European market, you have to affix CE marking to be allowed to sell it on the European market. And to affix CE marking you need to comply to (applicable) directives.

https://europa.eu/youreurope/business/selling-in-eu/selling-goods-services/selling-products-eu/index_en.htm


  These directives lay down the essential requirements that products have to fulfil.


It is a common misconception you need to comply to standards/norms. It is not true:


  The use of standards is voluntary - you are not obliged to use them. You can also opt for other technical solutions to fulfil the essential requirements set out in the relevant EU directive. 


However,


  If harmonised European standards exist for your product and you follow them in the production process, your product will be presumed to be in conformity with the requirements laid down in the relevant EU directives.


you're going to have a very hard job to prove conformity without using standards/norms.

Source of quoted text

So, doing EMC testing using harmonised standards comes closest to the proof your product is satisfying the EMC directive.