Not likely, Kate.You'd see it on your palms first - a V-shaped discoloring of the fronds down the centers.
Manganese is a trace element, so most plants don't use an awful lot. More likely your misshapen leaves on the other plants are due to the cold nights we've had. Those tropical divas don't like to get cooled off too much. Is that section of your garden maybe more exposed to the cold NW winds?