I assume that what you are actually saying is that you generated a new chiral center on an already chiral compound, giving you two diastereomers, and would like to know if the NMR signals are proportional to the amounts of the two diastereomers in the mixture? In that case, yes, the ratios of the integrals of corresponding protons should tell you the relative amounts of the two diastereomers. This technique is often used in reporting the results of assymetric reactions, where the chiral centers present in the starting material are used to influence the chirality of the reacting center.
And yes, usually if you see changes in the proton spectra between the two diastereomers, you should also see changes in the carbon spectra. Integrating carbon spectra is much less useful than integrating proton spectra, though, due to the wide spread in relaxation times among carbons in different magnetic environments.