Here is the list of tables that may effect with new INSERTS if you add new product in your magento.
You can use your own prefix instead of ayis_
ayis_cataloginventory_stock_item
ayis_cataloginventory_stock_status
ayis_catalogsearch_fulltext_scope1
ayis_catalog_category_product
ayis_catalog_category_product_index_store1
ayis_catalog_product_entity
ayis_catalog_product_entity_datetime
ayis_catalog_product_entity_decimal
ayis_catalog_product_entity_int
ayis_catalog_product_entity_media_gallery
ayis_catalog_product_entity_media_gallery_value
ayis_catalog_product_entity_media_gallery_value_to_entity
ayis_catalog_product_entity_text
ayis_catalog_product_entity_varchar
ayis_catalog_product_flat_1
ayis_catalog_product_index_eav
ayis_catalog_product_index_price
ayis_catalog_product_relation
ayis_catalog_product_super_attribute
ayis_catalog_product_super_attribute_label
ayis_catalog_product_super_link
ayis_catalog_product_website
ayis_catalog_url_rewrite_product_category
