If there are changes to the variant IDs, there are several possible effects:
the old products/variants should be kept around (archived or similar), otherwise Shopify will usually remove them from previous orders as well which means customers can't start a return for these orders since any reference to the product/variant is removed
temporary influence on Analytics Reports, some of these rely on the variant-id to tell variants apart
As you can see, there are some possible side-effects if changes to the variant IDs occur. Please feel free to contact our support if you feel that this is the case so we can confirm.