No reason why not as long as you have the travel in the mech to reach cogs 1 and 9. The mech largely just does what its told by the shifters, it might not be as smooth as a 9sp specific mech, but it will probably work.
You certainly can,the mech is physically the same,except the jockey wheels are slightly wider on the 7 speed mech.himano will tell you it does not work,but rest assured it does.Only 5 speed mechs are not compatible with 6,7,8, and 9 speed systems.
Just a quick addon question, will the 9 speed chains (narrower one's I see in the shops eg HG73 as opposed to the HG70) work on the 7/8 speed sprockets ? If so why are they narrower ?