Short answer. - - - NO, the stem would have no effect on the headset, either way.
Longer answer. The only relationship of the stem to the headset relates to the portion clamping on the steerer. Headset loosening implies something moving.
Sometimes we see crown races not properly seated, and causing loose headsets when they settle. In those csses, it's one or two and done when the crown race finds bottom.
Otherwise, the stem is sliding up a bit over time. Likely, it's not clamped tight enough, though rarely it's something prevent effective tightening.
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