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For all intents and purposes - no, not really. A digital camera can generally record outside sRGB space, but then you still run into gamut issues when trying to display let alone print the images. For computer display, things have improved with monitors that offer a large gamut as well. However, even then, you'll only really notice the difference on a side-by-side comparison. Which, of course, can still be a compelling argument to get the latest & greatest. If it wouldn't matter at all, these advances wouldn't exist. Is it something to lose any sleep over? Hardly.
No, it isn't, but (1) it doesn't really matter, (2) going into the question why not would be unnecessarily technical. Your monitor will happily display whatever colors thrown at it, within the limits of its gamut. Whether the colors come out as they should is a question of running color management-aware software.