How close? I have hand-held panos with objects as close as 10 feet and they are fine.It all depends on the scene.
One can align foreground parallax, or
background parallax, not both at the same time
. So if e.g. the background is not critical (no predictable structures) or blurred, or chaotic, one can align foreground features without trouble. However, parallax can turn out to be impossible to fix, or at least very time consuming, so it's still better to prevent than (having) to cure.
With a bit of practice (like turning oneself around the entrance pupil, instead of rotating from the neck or torso), and a good amount of overlap and good software, and a suitable subject (few occlusions), and some luck, it is possible to achieve good handheld results. But that was not the question the OP asked. Besides, good technique also requires fewer images (with less overlap) to achieve a successful stitch, which will save more time, especially when focus stacking or exposure bracketing enters the picture, so to speak.