Yes, they do, as long as the reservation has been made into a revenue booking class.

It's technically possible to use an MCO to pay the taxes, fees and charges on a redemption booking, in which case you would not earn as the underlying reservation is non-revenue.

in your case though, assuming that you simply use an MCO to reduce the cost of, or to pay in full for a revenue ticket, then all Avios and TPs relevant to such a booking will be due.