There is scant data on the effect of placebo on the autonomic nervous system and HRV in particular.  Since acupuncture research has a heavy burden of showing real effect versus placebo, it is of interest to note this study which finds no difference in HRV response between the control group and the placebo group.  This was NOT an acupuncture study.
J Evid Based Complementary Altern Med. 2015 Jun 4. pii: 2156587215588642.

[Epub ahead of print] Influence of a Suggestive Placebo Intervention on Psychobiological Responses to Social Stress: A Randomized Controlled Trial.
Zimmermann-Viehoff F1, Steckhan N2, Meissner K3, Deter HC2, Kirschbaum C4.
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We tested the hypothesis that a suggestive placebo intervention can reduce the subjective and neurobiological stress response to psychosocial stress. Fifty-four healthy male subjects with elevated levels of trait anxiety were randomly assigned in a 4:4:1 fashion to receive either no treatment (n = 24), a placebo pill (n = 24), or a herbal drug (n = 6) before undergoing a stress test. We repeatedly measured psychological variables as well as salivary cortisol, alpha-amylase, and heart rate variability prior to and following the stress test. The stressor increased subjective stress and anxiety, salivary cortisol, and alpha-amylase, and decreased heart rate variability (all P < .001). However, no significant differences between subjects receiving placebo or no treatment were found. Subjects receiving placebo showed increased wakefulness during the stress test compared with no-treatment controls (P < .001). Thus, the suggestive placebo intervention increased alertness, but modulated neither subjective stress and anxiety nor the physiological response to psychosocial stress.