What does "she was deploying her famous pipes" mean?

"Pipes" in this context means your vocal cords, or simply your voice. The singer's "pipes" are famous because she's a famous singer. To "deploy" her pipes means she sang.

"Set of pipes" or "pipes" idiomatically refers to the human voice, and indeed, the phrase focuses on the artist's singing in this scenario. In other usage, it can simply refer to a loud voice.

The word pipes draws an analogy to musical instruments, likely woodwinds such as a flutes, oboes, or even bagpipes.

This expression means something like 'engaging her singing equipment', with analogy (pipes) to a modest-looking but loud church organ. The woman in your question is evidently renowned for opening her normal, human-sized mouth and producing a disproportionately gigantic (and probably tuneful) noise. It can be used sarcastically to indicate tuneless volume.

It does not refer to vocal chords (which are vibrating flaps in the throat that control pitch), but more to the entire human air-pumping assembly, with particular suggestion of the lungs, and with special regard to singing. I have never heard it used to refer to mere shouting.

I have also only ever heard this expression applied to women, although to my knowledge there would be no reason not to apply it to men as well.

I once got into trouble by observing to a girlfriend that a woman singing Nancy in a production of Oliver! 'has got some pipes on her', meaning that her effortlessly mellifluous singing dominated the rest of the cast, the orchestra, and the Edinburgh traffic. A passing airliner would have had its work cut out to compete. My companion assumed, however, that I was making some sort of sexual observation.

It seems clear, therefore, that the expression is a common one in performance circles, but perhaps not in wider society.

It primarily connotes volume in singing, ideally with tunefulness attached.