It's always a good idea at the very least use a surge protector. We have UPS units for all our gear so we can properly shut down our equipment if there's a power outage while we're working. That happens more often than we like in our area.
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Because the ac is converted to 12dc I doubt it would damage anything. Most of these camera power supplies have a very wide input voltage range. If you are capturing, John's routine is a sound one. A power failure could cause problems with captured media during this process like the manual warns.
"thou can not stir a flower without crumbling a star" ......Henry Wadsworth Longfellow