As you all are most likely aware of, it is possible to import any SHA256 hash as a bitcoin wallet private key. You can generate SHA256 hashes on this website: http://passwordsgenerator.net/sha256-hash-generator/
No, you can't just make a hash out of a password, smack it into any client and expect it to work.These are the steps to convert it into a private key: https://en.bitcoin.it/wiki/Wallet_import_format. That being said, its incredibly insecure to generate an address using SHA256 since its rather fast to bruteforce tons of address with weak to moderate passwords.
Is it possible to check on an offline computer which bitcoin address it corresponds to? I'm thinking about creating a brain wallet on an offline machine to store bitcoin on. Thank you for any help 
Yes, there are various scripts to do so, eg. Bitaddress.org.I really cannot recommend anyone generating an address with a password and expecting it not to be compromised in a short time. You can generate addresses on Bitaddress.org, don't use the brainwallet function.
If you use bitaddress.org, you should generate the key under an operating system that uses isolation techniques to guarantee that the OS is no infected with any malware and whatnot.
Tails is very easy to install. I have only used it to create paperwallets. Just put Tails in a DVD, launch it and after it boots just open the browser, go to bitaddress, then turn off your modem and generate the key, that's all.