If the magnetic field of Earth is generated in the core of the Earth can we deduce core's precession cycle by measuring the precession of Earth's magnetic field (not Earth as a material object) or the two features are not directly connected?
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The precession an nutation of the Earth happen on an timescale of thousands of years.
The convection precesses in the Earth's mantle happen on a timescale of tens of millions of years.
Those timescales are so far apart: any influence is negligable. That means that for the precession and nutation of the Earth the Earth is treated as a single solid mass.
Geologists have established that the geological record shows that the Earth's magnetic field has switched polarity many times. The transitions occur geologically speaking fast, over a period of several thousands of years.
To my knowledge there has never been a suggestion of some connection between the processes of precession and nutation, and the processes underlying the Earth's magnetic field. Such a connection is very, very implausible.
How the Earth's magnetic field is generated is still only partially understood. Presumably there is a connection with the convection processes in the mantle, but as I said, still only partially understood.
Correction in response to a comment:
After a quick search: the Earth's core is thought to be differentiated in a solid inner core and a fluid outer core. The modeling suggest that the outer core has convection. By the looks of it: there aren't estimates of the rate of that convection.
The supposition is that convection in the outer core layer is a necessary element of the processes that give rise to the Earth's magnetic field
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$\begingroup$ I've been under the impression that the magnetic field was produced by convection processes in the conductive core rather than in the mantle. $\endgroup$ Commented Nov 1, 2020 at 18:37