Technically, the order will go through, but you won't receive any rewards for it: self-referral purchases are prohibited by the affiliate program rules.
How it works
Purchasing through your own link is considered a self-referral and violates the program rules, so no commission is awarded for such an order.
What happens to the discount
The promo code discount is applied as usual — you just won't receive any additional affiliate reward.
Please note. If an order appears in your statistics with zero commission, check if it was placed from your own account. How to view earnings is described in the article How much does the affiliate program pay.