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Yes, diffraction blur is larger, relative to the full image size, at f/5.6 on a small sensor camera, compared to a large sensor camera, as the absolute size of the analog blur is the same at f/5.6 with all sensors. That said, f/5.6 on a small sensor doesn't necessarily mean a hopelessly soft image, that can't be sharpened if ISO is low, and since most small sensors don't have AA filters, they need some diffraction to avoid aliasing.
Diffraction at f/5.6 on a small sensor is not a problem at all if you aren't going to be cropping into the full image; the extra blur is generally very small relative to a full image downsampled to a monitor screen.
Most figures that you will see quoted about "diffraction limits" sound a lot worse than they really are, and are usually calculated or interpreted in the wrong way.