Encrypting with Private Key

[utternoncesense at gmail.com]

Does GPG enable me to encrypt a file with my private key?  Obviously
it encrypts hashes with my private key for signatures, I'd like to do
it for a file.

And yes, I realize that this provides absolutely no security, and yes,
I know I could more efficiently prove a file came from myself by just
encrypting the hash/signing the message.  So it's mostly an academic
question, but I'm curious because I didn't see the option on the man
page.