Illegal? No.

Violation of DD TOS? Absolutely.

Existing customers ("Referrer") who refer friends and family as new customers ("Customer") to the DoorDash platform, may be eligible to receive referral credits (“Credit(s)”). Customer must sign up using the unique link ("Link") provided to them by Referrer. The Link must be provided to Customer through email, text, or the Share Your Link option on the app. Referrer is prohibited from posting referral links on sites including, but not limited to Google, Craigslist, Twitter, RetailMeNot and other similar publicly accessible sites. DoorDash reserves the right to deactivate or invalidate any Credits obtained through these channels.

In the Q&A about the referral program, DD specifically states that:

Your referral link should be shared with people you know personally.