When you hit with a dual wield heavy attack, both weapons can procs their enchantments. However, enchantment types do not stack and have a cool down...usually five seconds. So if you hit with a fire enchant, you have to wait five seconds before any fire enchant on any weapon can hit. Therefore in a heavy attack double proc scenario, the second weapon can not proc when the computer processes its hit. However, if you have a fire enchant on one weapon then a frost on the second and complete the same heavy attack, they can both proc...starting a five second cool down for fire AND a five second cool down for frost.
So in your scenario, no...you can only have one weapon damage active at a time. So enchant the second weapon with something else.