I think no, because when you use a remote node you are allowing the remote daemon to select the other ring members for your tx, so a malicious remote node could determine your real tx output, and also link that to your IP if you weren't using a VPN or something. I think your best bet for privacy is to use your own daemon and broadcast the tx over Tor. (Disclaimer: I'm not a privacy geek and haven't actually done any of these things except use a remote node.)
Are ring members chosen by the daemon, not the wallet?
How can you select other dummy tx outputs to use in ring signature if you don't have a copy of the blockchain containing other tx outputs? I'm fairly certain yes, the wallet requests ring members and the daemon returns them.
