While the Algolia extension does not monitor checkout continuously, it does monitor stock changes, which can get triggered after shipping the product, for example.
A change to stock will cause the affected object ID for the product to be reindexed to Algolia, if the extension observes changes in indexed attributes such as order_qty , stock_qty or in_stock .
Note that it's possible to implement your own observers on events such as sales_order_shipment_save_after and checkout_submit_all_after and perform indexing based on these triggers, but the extension does not do this by default. Because of the nature of the queue, it could run the risk of flooding it, so careful testing is advised when implementing something like this.