Yes, but it wouldn't be a very wise move financially. After all, you'd still be paying taxes on the money that you deposit.
If you wanted to do direct deposit, all your employer needs is a voided check from your friend for the numbers at the bottom.
If you get paid in draft form, simply endorse the check over to your friend for them to deposit.
I can't think of any reason why your employer would care to whom your paycheck went to.
(I used to have $250 deposited into my parent's checking account as a stipend each pay period at one point and no one even so much as raised an eyebrow when I did it.)
That reminds me, there could be some tax implications because at least in the IRS your paycheck would be considered a "gift" to your friend and you'd need to report the transaction.