Am I at risk of damaging my Keurig machine if I place an ordinary black tea bag inside instead of a K-Cup?
It will not damage the machine; However, it won't brew properly. Your tea is supposed to steep inside the water for a set period of time; but the Keurig will simply pour water quickly through it, resulting in extremely weak tea.
So no, it won't damage the machine, but you will not brew your tea correctly.
Actually, The reason the Keurig machines can brew tea so quickly is because both K-Cups and the My K-Cup add the element of pressure to the steeping equation. This pressure speeds extractions in ways low-pressure steeping does not, meaning the compounds in tea are extracted faster.