Probably a question that should be answered by DH, but I'd guess the answer is no.
Promo code wouldn't be used on something that's free.
10% of 0 = 0
So, I doubt one time referral payouts would go through... but you never know.
Also, what if you refer someone, get paid for it, then they prove non-profit status within the first 97 days... is that a refund? I would guess that would be a yes.
I'd guess they'll do some tweaking on the referral code to work with the free non-profit accounts, if they haven't already.
Save up to $96 at Dreamhost with ALMOST97 promo code (I get $1).
Or save $97 with THEFULL97.