I've tested this in both my 2015 and my 2017 key-less Sonatas and both of them allow you to drive off without the key. Start car, threw key into grass, shut door, got no key found warning, shifted to drive, and drove down the street. I remember reading complaints about this somewhere, I wanna say NHTSA, back in 2015 since there are standards they enforce about not being able to take the car out of park without the key in it. they haven't fixed it in my 2017.
As for OP, check out the k5os CCM if you want to add this feature they call it stop-and-go, and a hundred other ones, to your car after market. I've put it in both my Sonatas and love it.
https://www.k5optimastore.com/products/k5os-canbus-control-module