Yes and no. OH/NH peaks are removed when added D2O, yes. However D2O doesn't have extra protons, but rather extra neutrons.
The H from OH is transferred to one of the lone pairs of O in D2O, forming an alkoxide ion and HD2O+.
The alkoxide ion will react with unreacted D2O to reform the alcohol [plus and OD-], except the group is now OD and not OH.
HD2O and OD- will just get lost into normal equilibrium with water (H2O or D2O), so we don't have to worry about them.
i.e.
CH3CH2OH + D2O -> CH3CH2O- + HD2O+
CH3CH2O- + D2O -> CH3CH2OD + OD-
[no OH peaks produced because there is no OH, but rather OD]
I don't think we need to know why OH/NH peaks are removed when we add D2O at A level, but there's the little explanation if anyone else is curious.
If anyone else has anything I may have missed/wrote that doesn't seem right, please say !