I have on rare occasion wondered if woodpeckers ever perch like "normal" birds; it's not something you see them do often, if at all. I do not find my lack of personal experience of woodpeckers sitting with perfect posture surprising, as their feet are actually structured slightly differently than those of passerines, the so-called "perching birds". Songbirds have three toes that face forward and a fourth that faces backward; woodpeckers have two toes that face forward and two toes that face backwards (which makes them "zygodactyl"). This two-and-two layout is an excellent set-up for scrambling up and down trees, but does it interfere with the ability to perch upright?
"Nobody here but us sparrows…"
Apparently not. This Downy Woodpecker had been feeding at a highly-exposed suet feeder. I'm guessing that a hawk appeared somewhere out of my sight, because while I was watching he dove into the closest cover (such as it was) and froze in this position. You can see the two-toed front-and-back grip he has on the branch.
Yup, they can perch upright, albeit awkwardly. Not that it's an effective evasive technique when your plumage is a bold black and white with a big red target on the back of your head; he may have been better off clinging vertically to the far side of a tree trunk (a woodpecker's most effective and oft employed evasion tactic).
[To the best of my knowledge, he did not become lunch. Nor did he remain sitting upright for any longer than necessary...]