At the very least, you can manually set the style to match the indicator. If you inspect the indicator styles and copy them all, you can get pretty close. The text size won't be responsive, but you can set it to something pretty big.
<p style="display:flex; flex-direction:column; flex-shrink:1; flex:1 1 auto; font-size:72px; justify-content:center; margin-bottom:1.5rem; margin-left:1.5rem; margin-right:1.5rem; margin-top:1.5rem; overflow:hidden; text-align:center; border-color:#dfdfdf; box-sizing:border-box; color:4a4a4a; font-weight:600; line-height:normal; stroke-width:2">No Data</p>
Just copy and past that HTML into your No Data formatting (be sure to click "source" first), and you'll be pretty close.
On the left, an indicator, on the right, formatted "no data" text with the above HTML.
- Josh Carlson
Kendall County GIS