No, it can be done on demand, but it still can take time. You can either social engineer the victim or a sysadmin for the email service (probably not very easy for something big like gmail), or compromise the victim's computer in another way so you get their email credentials (browser exploit, media exploit, or even just malware sent via spear phishing). Punycode abuse works wonders, too.
A particularly sophisticated attacker (pretty much anyone who has information resources on par with Raytheon SI like a state actor or another defense contractor) can hack into the actual server on demand through IPMI, poorly secured routers, stuff like that. Just look at all the Yahoo email hacks. For an "average joe hacker", the most effective method would be targeting the individual, not the email server.