Yes any bag can be used as a diaper bag.
The diaper bag is just needed to carry diapers, wipes, bottles, toys etc or any other things needed to change your babies diaper.
I also recommend keeping a few outfits available to change the baby or toddler into should their diaper leak on the clothes.
I've always kept a few sets of baby clothes in a diaper bag which I used a backpack for which held more than a diaper bag could hold.
I kept a pack of diapers in the car as well so that I had enough diapers in case we got stranded somewhere and needed more diapers.
A good backpack is a better option for a diaper bag so you can put extra clothes in the diaper bag as well.