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?
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