Rond Vidar is a member of the Legion, and his only superpower was having a Green Lantern ring. As Stsword mentioned, he was Universo's son, and he got an 'honorary membership' for helping thwart Universo, and then later became a full member as a Green Lantern. Thus, there's precedent for Dana Dearden joining the Legion depending on the situation. Odds are good she'll want to help thwart the Time Trapper since the timeline she came from no longer exists and all, and that'll probably get her foot in the door.
I thought they loopholed Rond Vidar, that his qualifying power was that he had the willpower to resist the superhypnosis of his father, and presumably similar mind controllers. So his power was "super willpower."
Actually there's another possible rule that might prevent Dana from being a legionnaire. And this rule I find silly- Every legionnaire is required to have a unique power, unless you have the kryptonian package. As if potentially useful legionnaires not being on a mission for whatever reason didn't happen all the freaking time in the stories.
The coins give her strength, speed, flight, supervision, electricity, and durability. The legion probably has all of those covered.
It was a plot point when Wildfire tried to join up. He auditioned with powers that Mon-El, Shrinking Violet, Colossal Boy, Phantom Girl, and Chemical Kid all had. He didn't learn how to release his anti-energy for energy blasts without leaving his suit until later, so he refused to show that power. Then he uses it to save Colossal Boy's life, and the legion, not realizing he wasn't dead, jacked his suit, so it took him a while to fly back to Earth and find his suit again.
And was why Lightning Lass's powers were altered to make her Light Lass instead- her brother decided to return to the legion, and two lightning throwers was one too many, according to the rules.
Of course, none of the legions ever shown were the legion of superheroes of Earth-16, so Zoat is perfectly free to jettison both rules as silly if he so desires.
Heck, he could have the founder of the Legion of Superheroes, Brande, be the Martian Manhunter like DC comics once decided on but was never shown.