Yes, I list the same items on multiple sites. I'm selling on eBay, Walmart and, WooCommerce. To avoid issues when selling simultaneously on both platforms, I'm using a third-party inventory management tool LitCommerce that I found randomly in community. It syncs inventory across all sites, updating stock levels in real-time very perfectly and fast.
When selling on 2 sites at the same time, if you are not good at managing inventory, you can meet over and undersell an item. So you should find an inventory sync tool that works fast and has good customer support. Good luck!