It depends on what you want to sync. If you just want to sync the inventory levels then there is nothing to worry about regarding the variants. As long as the SKUs match on each system then the sync should run smoothly.
It will be a problem if you want product information (title, description, price, etc.) synced, as then we will have to change the structure on both systems. This means that the BigCommerce products will have to be in simple product form, instead of as configurable products. Meaning, each variant will have to be a separate product with its own SKU, rather than being grouped under a parent product, much like the way VendHQ products are listed.