No and yes. Firstly the no. Some software is programmed to check the number of cores in a CPU and will not function if it does not find the number it needs.
Now the yes. Software will make use of whatever resources available, one to twenty cores, whatever. However, if the number of cores to handle parallel threads is insufficient, although the software may run, it will run very slowly. for some applications, slow is merely annoying, for games, slow can be completely unplayable.
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