No. We don't keep a copy of your connection secret. It's only created locally in your browser. That way, if we ever get served a warrant to hand over anyone's details, we won't have any details to hand over.
Leaving your connection in your browser is convenient, but does mean that anyone that has access to your browser can get access to your wallet.
We recommend loading your NWC connection into Zeus or AlbyGo. You then have a fully functioning lightning wallet. You can turn on PIN or fingerprint security in both those wallets which is much more secure.