You had me worried there for a second, Corazon
Nah it's perfectly OK the way the op plans to do that.
USB can address up to 127 devices (IIRC) but the power transmitted through USB is very limited so an externally powered hub is the way to go.
Just make sure to use a high quality USB cable at least between computer or box.
And make sure you build some means of cooling ( like a couple fans...2 in one out) into that box. 4HDDs in confined space might generate some heat