Yes, briefly.
For all features, Document Intelligence temporarily stores data and results in Azure Storage in the same region as the request. Your data is then deleted within 24 hours from the time that you submit an analyze request.
For trained custom models, the interim outputs after analysis and labeling are stored in the same Azure Storage location where you store your training data. The trained custom models are stored in Azure Storage in the same region, and are logically isolated with your Azure subscription and API credentials.