It appears that functionality here is somewhat dependent on the display and on the software driving the video card.
On my G5 (PowerMac 11,2), with a GeForce 6600 LE connected to a Dell U2415 monitor with a Amazon Basics DVI-to-HDMI adapter, I’ve observed that video output doesn’t show on the display while in firmware (ie: chooser, of prompt), but does work once OS X (at least the installer) begins to boot (showing the Apple Logo onwards).
I’m not sure there’s a way to resolve this: it’s likely there is some issue in the GeForce 6600 LE rom that is used in openfirmware when used with my Dell U2415 display. Changing either of these might help, but I don’t have a different graphics card or display to try with.
I’m planning on using a DVI to DisplayPort active adapter (StarTech makes one) to work around the issue.