Yes, it absolutely would. As would trapping focus so you can't tab back to the rest of the page (since it is designed as a modal).
The entire navigation interface needs a keyboard accessibility overhaul to comply with these recommendations:
Want to make an issue for that larger project?
I was already thinking about doing some menu overhaul and working on the RS bust menu (how it gets populated, reintegrate some of the old personalization options). If no one has tackled keyboard nav in the UI before I start that (likely a summer project), I would be willing to combine the two.