That is a situation that could potentially work.
8 speed chains are slightly thicker then 9 speed chains. What you might find is that when you are in your middle ring, your chain might rub or catch on your big ring, which may lead to chain suck. Same when you are in your small ring, your chain might catch on your middle ring. Also, it might be kind of tricky to set your front shifter up to properly, assuming your shifter is for a 24 speed drivetrain.
That is worst case. It could also go error free. Chainrings and front derailleurs can be mysterious things at times.
If you get the crankset, and you are having problems, you would probably be able to solve the problems with washers. 1 metal washer on each bolt point, between your crank spider and middle chainring. 2 metal wasters on each bolt point between your crank spider and small chainring. This will spread your chain rings out a bit, so they will be compatable with your thicker chain and 24 speed shifter. You can experiment a bit with the thickness of the washers to fine tune things.
Cheers,
Juba