Short answer--yeah it would work.
If you do some research on Deep Water Culture (DWC) you'll find lots of bucket systems like yours.
Also, since the "deep" part doesn't necessarily apply to your situation, you could make it into a dripper system, or a modified Flood-and-Drain system.
There are as many variations as one can dream up. Most of them will work. Do some searching both here and elsewhere and you'll find all the info ya need.
Good Luck.