I'd almost have to read the question, but my gut says check "no" if it asks specifically about a conviction. Keep a screenshot of the application language.
But what kind of reckless was it? Some states specify a "wet" reckless which everyone knows is a watered-down DUI. Personally I'd probably check yes if the reckless had any kind of formal characterization related to DUI.
They will likely ask about other moving violations, and any reckless conviction will obviously merit further discussion at an interview. Checking no while explaining in the addendum might help you get past the computer filter to a human.