Yes you can see most of your data without a cloud connection. But some features are limited and require the subscription. A google account is required though to use the app I believe.

Of course, getting more than a snapshot of the data is a bit of a pain. Fitbit has a developer portal and you can create a dev app key to export your data. There is at least one open source project that pulls this data down regularly and feeds it into grafana. I'm not sure if the pixel line of watches provides a similar developer portal.

EDIT: actually, you said cloud connection. I think in this case the data is still being sent to the cloud, hence the API to fetch it. But you don't have to enable sharing with other services or purchase the health subscription. So maybe the answer is still that no, you can't really do much without the cloud connection.