In this work, we report a theoretical study based on quantum transport simulations that show the impact of the surface roughness on the performance of ultimately scaled gate-all-around silicon nanowire transistors (SNWT) with precisely positioned dopants designed for digital circuit applications. Due to strong inhomogeneity of the self-consistent electrostatic potential, a full 3-D real-space Non Equilibrium Green's Function (NEGF) formalism is used. The individual dopants and the profile of the channel surface roughness act as localized scatters and, hence, the impact on the electron transport is directly correlated to the combined effect of position of the single dopants and surface roughness shape. As a result, a large variation in the IOFF and ION and modest variation of the subthreshold slope are observed in the ID-VG characteristics when comparing devices without surface roughness. The variations of the current-voltage characteristics are analyzed with reference to the behaviour of the transmission coefficients, electron potential and electron concentration along the length of the device. Our calculations provide guidance for a future development of the next generation components with sub-10 nm dimensions for the semiconductor industry.