Yes, its usually on a DVD (safer because it cant be modified) or USB (more convienient as it allows to store extra data) and is booted into your memory. Thus it does not access your HD because its not actually installed. As long as you trust the hardware you could use it on any machine, even an infected one. The only problem I currently see is that you have to get electrum once you booted tails, but that might change with the next version [2] of tails.
[1]
http://doc.satoshilabs.com/trezor-faq/overview.html[2]
https://labs.riseup.net/code/issues/6739Can't I just install electrum on tails, and save it? So I don't have to get it everytime? I am not sure if I understood your last sentence.
You also talked about multisig, I don't understand what it is. Could you explain it briefly?