You can transfer a .GR or .EU domain to Papaki whenever you feel like it, even if the domain names is in quarantine. However you cannot transfer .COM, .NET, .INFO, etc. domain names, while in quarantine state.
The domain transfer procedure takes 5-7 days, so it's better not to wait until the last minute to transfer your domain. See which domain name features you get with your domain at Papaki.