Does installing proprietary hardware drivers onto a Debian system disable my right to run/use it for any purpose?
Or, as an example, can Debian be used to prepare paid Linux courses if proprietary drivers are installed?
It will depend on the proprietary licence on the driver. Most commercial software comes with certain restrictions on its operation and use; for example, Microsoft's standard terms provide that "Customer may not (and is not licensed to) use the Products to offer commercial hosting services to third parties".
If you had installed a proprietary driver that included a licence term that said, for example, "Customer may not use this Product in any part of an educational process", then if the preparation of your (paid) Linux course used the hardware that used that driver, you might well be in violation of the licence.
This is not a free software issue, except inasmuch as if you start installing random bits of proprietary software onto your hitherto-free system, you can start loading yourself up with all sorts of unpleasant licence terms. Don't do that.