We pollard willows regularly here, and when I saw this question I was thinking that I'm not sure they use less water when you pollard them. And then this exressed what I didn't know how to say.
Cj Verde wrote:
There are lots of good reasons to coppice but I haven't read that reducing water needs is one. I do know that coppicing favors leaf growth over woody growth & leaf growth might need more water, not sure.
After pollarding you have to give plenty of water to get a nice lush spurt of green leafy tender growth. I don't know what would happen if you didn't, but I think the tree wouldn't be vigorous.