It could be, but it's more likely to be an unhelpful distraction, providing temptation to engage in fallacious reasoning and character assassination based on pre-existing prejudices with little to no actual evidence. It's more work to consider what a measure captures and what it doesn't, and whether there are systematic factors that deferentially affect how different demographic groups appear under the measure--more work, but actually useful. If that shows a huge effect, then a possible follow-up question is whether the huge effect was intentional, especially if whether it was intentional or not impacts one's prospects for fixing it.

Still, if one wanted to know: the h-index was proposed by the condensed matter physicist J. E. Hirsch of UC San Diego; he's originally Argentinian and is interested primarily in how microscopic properties yield bulk effects like magnetism and superconductivity.

Just like you'd expect of a physicist, he took a complex problem (in this case, one that everyone in academia grapples with all the time, which is "how do we assess quality?") and, through a variety of oversimplifications, came up with a single number that at least sorta got at the answer. As he said in the conclusion of his paper, "I suggest that this index may provide a useful yardstick to compare different individuals competing for the same resource when an important evaluation criterion is scientific achievement, in an unbiased way."

So, there you go.

But, anyway, I was comparing Dr. Gay's output to people in a similar demographic, so I already took that part of your comment into account. (One could also note that people have done studies of racial bias in citation, and found that there is an effect, but even the largest effects measured would be unlikely to move Dr. Gay by more than 30% or so, still leaving her in decent but unremarkable territory in terms of scholarly impact.)

You can find the original h-index paper here: https://arxiv.org/pdf/physics/0508025.pdf

Her credentials sufficed, as you said, and it's likely enough that the reason her academic credentials do not appear stronger is that she was drawn more to administrative work: she took the role of Dean of Social Sciences starting in 2015.

Nonetheless, if you're going to sing her praises, you probably ought to first find out enough about her to know what tune to sing.