Out of the box, no - but that's the beauty of Magento, its a modular platform you can extend to suit your needs.
You would have a few options for implementation (which would largely depend on the actual design requirements for the frontend of your site).
My advice would be to deliberately not include stock levels within the rendered HTML, and include a post-page load Ajax request to your stock system. This is a great way to ensure a quick TTFB and reduces the burden on your Magento server for stock lookup. Use simple JS validation to prevent adding to cart if the stock level is below zero. Then on the checkout, tie in proper server-side validation into the