If you're just mirroring your screen it should be fine. If it's set up as another monitor there's no reason it wouldn't work.
I could see some issues comeing in if you were trying to use something like parsec, or discord, or some third party app for your projector.
You can also usually get around the black screen thing by just disabling your hardware acceleration in your browser. It doesn't do much in my experience unless you're trying to render/simulate stuff.
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I could see some issues comeing in if you were trying to use something like parsec, or discord, or some third party app for your projector.