Do differential i/p need to be clamped?

marksanders said:

You are correct that the C cannot charge up due to the low resistance of the secondary winding that would always discharge it. This is a mistake on my part.

However any DC bias currents flowing in or out of the + or - amplifier inputs have no route to 0V. All of the protection diodes would be normally be off, apart from leakage currents, at the normal voltage levels at the + and - pins of the differential amplifier around about 0V.
The capacitor will provide some filtering of the transformer output signal and reduce the bandwidth at some point.

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