How good is AutoHDR at matching bracketed shots with a bit of camera shake?

Exceptionally good. Many photographers shoot handheld with no problems — the alignment process makes handheld shoots look like they were shot on a tripod. The one thing to avoid is blur within a single bracket from shake during that exposure.

Alignment is robust

Misalignment between brackets is fine — the AI corrects for it. Handheld shoots can look indistinguishable from tripod work after processing.

What it can't fix

If a single bracket is blurry due to shake during the exposure itself, that blur stays in the output. The AI aligns frames but can't sharpen motion blur in the source.