Does an unopened encrypted Electrum wallet relay its addresses/transactions to nodes? I have Electrum 3.1.3 (windows) installed with an encrypted wallet, which is accessed over a VPN.

The Issue:

I accidentally opened the Electrum program without VPN protection, but the encrypted wallet (default_wallet) wasn't opened (i.e. I didn't enter the wallet password to open it).

So, is there a chance that the wallet addresses got relayed to electrum nodes with my non-VPN ip-address and in turn got compromised?

Reason for the question

When the Electrum program was clicked open, a lot of network packets were send &amp; received, even though the wallet wasn't open.
No because until you provide the password at the start Electrum can't decrypt your wallet file so it doesn't know your addresses and can't query a server about related transactions. This only applies if you are using full wallet file encryption. You know you are doing that if you are asked a password at the start and not just when you try to spend your coins. 

Another way is to go to wallet menu > password. The encrypt wallet file option should be checked there. A third way would be to go to file > save copy and examine the saved file in a plain text editor. If you find that it's all random unreadable characters (ciphertext) and not JSON code then you have full wallet encryption.

BTW you can configure a socks proxy under tools > network > proxy tab. If you configure a socks proxy that can only be accessed via your VPN you will never make the mistake of connecting without a VPN. However, note that a VPN does not anonymize you. It just prevents censorship. If you want anonymity use Tor but also note that all bitcoin transactions are public so it can never be truly anonymous.