Regardless of pixel size, it is true (even for film) that for a given size print, the optical image recorded by the camera will have been enlarged by a factor of 1.6 in each dimension more than the FF version of the same image. So optical imperfections will also have been enlarged that much more. Whether they become visible will depend a lot on the size of the print. The effect of diffraction is also subject to print size (and viewing distance etc) as to when it become visible - these are all related to the same geometry that drives the difference in DoF. (sensor : print size ratio). The pixel size comes in mainly when people think "I want to print at 300 ppi" for example, and compare images from cameras with pixels of different dimensions and forget that they are geometrically enlarging the image from the small pixel camera more than the large pixel camera, and aggravating any optical flaws at the same time. Like "I went from 13 MP to 21 MP in my FF so I should be able to print larger because I've got more pixels". True to a certain extent, but the same image is being enlarged more so flaws become more likely to be visible. The best large landscape prints come from the larger formats (8x10>4x5>MF>FF>crop>MFT>P&S).
Diffraction effects, DoF effects, motion blur (camera or subject) are all dependent on how much the image is enlarged after capture. Obviously other factors play their roles but this one is often overlooked So you need to specify print size to know how important all these factors are