since the curing of a polymer is nothing else but the bulid up of a 3D-network this means that the chemical bonding of the monomers and especially of the of functional groups chance. This leads to a change of the probability density of the electrons within the polymers. This should finally lead to a changing signal of the NMR spectrum.
Curing of polymer leads to structural changes via cross linking. Thus 1H- NMR or 13C-NMR would certainly be different for a polymer before curing and after curing. As the chemical and electronic environment of protons or carbons changes the chemical shift and coupling constant also can change.
The magnitude of the difference will depend on the crosslink density. If the are few crosslink sites in the sample, the proton NMR will be dominated by the linear material.