Is it possible to determinate the unspent balance of an arbitrary bitcoin address (not one from my wallet) from the Electrum console?
yes use getaddressbalance("address") - Note I only use electrum for litecoin but should work the same for bitcoin. Also the address used below is not mine but a random one from a litecoin blockchain explorer.
>> getaddressbalance("LiEMRo8aYs7iHQzRPpUF3GGG3xmgEGJLrr")
{
"confirmed": "16103.49132166",
"unconfirmed": "0"
}