Not really.
This UI toolkit is based on GPUI library build by Zed editor team, and while they improve accessibility over time (like, improving contrast and stuff), it's opaque to screen readers.
At the moment if you want to have good accessibility story you should probably look at Slint or Qt (via cxx-qt, for example). And since System 76 picked up Iced for their UI it should receive a11y-related updates, too.
System76 runs their own fork of Iced and commits things back to Iced, but in practice this hasn’t been as much as people seem to think.
Accessibility falls under this: to my knowledge Cosmic has it, Iced does not.