Yes, you can with your Nextcloud server configured:
You also can do not host the Tardigrade S3 Gateway for the Nextcloud server, but use a Gateway MT (hosted solution as a service) instead:
But keep in mind - the Gateway-MT uses server-side encryption unlike Tardigrade S3 Gateway (you should host it yourself alongside with the Nextcloud server and it uses a client-side encryption).
If you need a client for Tardigrade, you can use FileZilla (but you cannot share links from it at the moment) or integrated web-interface of the Tardigrade S3 Gateway on http://localhost:7777, you can share links from it, but you then should expose it to the internet with SSL via reverse proxy for example.
Another way is to use experimental web interface: