Yes, I think "hide" is the more proper/specific term. Thank you.
A "close to tray" option has been implemented in numerous existing apps that offer a systray/notification area status indicator icon. It's apparently done in a window manager agnostic fashion. I.e. I get the same toggle-able option with such apps regardless of whether I'm displaying them via xfce, fluxbox, enlightenment, &c. This isn't some new idea I've come up with, I've been coming across implementations of it for years in other apps.
As mentioned, I just recently saw (and used) such in the DeadBeef audio player. Here's a screenshot, taken just moments ago, of the same option being offered in the Audacious audio player as well:  (next to the mouse pointer)