In my humble opinion: Not if you like the way it sounds. A convex back will be stiffer than a similar flat section and will respond differently acoustically. In theory, you can also reduce bracing in an arched back (or top, for that matter). Bracing is both structural and aids in voicing the instrument, so it's the totality of the system that counts.
Convex backs and tops can also help avoid cracking/splitting in solid woods. Wood expands and contracts with variations in temperature/humidity, and a convex shape gives it somewhere to go with less stress. As an example, a flat back is pretty much trapped by the bracing and sides of the instrument. When subjected to low humidity the back wants to shrink -- particularly across the grain. At some point the wood is going to split (or part from the sides). In a convex back the same thing is happening, but there's more room for error because there's more wood there -- the back will flatten out some, but probably not to the point of splitting.