Yes.
I believe that data is encrypted before being sent to the server.
edit: see https://bitcointalksearch.org/topic/online-label-syncing-plugin-in-electrum-17-154144
Oh... doesnt sound good... I mean who knows what those data could be useful for if such a electrum server gets hacked or seized. And the server operator could see it all the time. The same goes for the plugin server.
So its possible to identify the complete wallet, addresses, transactions and property of a certain user only by finding one hint. I dont like thinking about this and im a bit angry why i didnt think about this earlier.
I thought it would be better to create a new wallet and a new plugin account with new email sometimes. But now i think using electrum is a risk in itself. You need to trust every server provider (when using auto connect, which is the standard) and you need to hope the server nor the plugin server gets hacked. Sounds a bit risky. The coins cant be stolen but it sounds still too much for me.
You can run your own server if that is bothering you so much.
You mean, an Electrum server?