From a web service perspective, these users are simultaneously. A dual-core processor can easily switch between 1000 threads; in most cases, the stream will wait for network I / O, so it is very similar to how it will work if you actually had 1000 cores.
So JMeter should be fine. It is possible that if the test thread must carry the load of working with an intensive processor, this may lead to bias in the results. But usually test threads just wait for an answer.
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