Is it safe to mount garage wall storage units to drywall panels?

Yes, it is safe to mount garage wall storage units on drywall, if you do so correctly. Assuming standard aluminum stud/drywall techniques, it means that you have 16-inch studs on 16-inch headers. This means that if you put a metal screw into the studding at 16-inches and a second a foot or two below, then you have a very stable anchor point. Now, assuming that your storage unit is 60 inches wide by 60 inches deep then you will have as many as five studs available to handle the weight of the unit and any equipment you may keep inside. However, unless you're planning to store a small semi/tractor rig there, using three of the five studs available is a great way to handle this.