Nope. Their browser seems intended to be paired with their VPN product, not to be substituted for it.

In my understanding, the Mullvad VPN extension is built in, with Mullvad DoH included.

https://mullvad.net/en/help/tag/mullvad-browser/#93

Does it offer the same system-wide protection as the desktop VPN product; or, does it only use the VPN for socks-proxied traffic through the extension-created SOCKS port, and so those protections are applied within the browser; or, it doesn’t protect against temporary interruptions; or, orher?

I can’t experiment with this during my workday, and we’ve reached the limit of information available without running it and testing, so I can’t help resolve this further right now.