Yes. QuickBooks Commerce calculates SoH values in-app and sends/syncs the values at the end of each day (i.e., midnight) to QBO, wherein an SoH ledger will be created.
However, do note that QuickBooks Commerce does not integrate with QBO’s Inventory Management. So if a Variant is created in QBO, it will not sync back to QuickBooks Commerce, including the stock level assigned to it.