Is it possible to use Vanitygen to create a paper wallet?
Could I put a copy of Vanitygen onto a USB stick and run it on an offline computer to generate an address and private key (which can then be printed onto paper)?
Yes, the source of the private key is irrelevant for a paperwallet. You could theoretically use the private keys from your hot wallet. That would not make much sense from a security point of view though.