There are some practical losses in efficiency from voltage conversions and such (a capcitor's voltage is proportional to the square root of it's stored energy,

There are some practical losses in efficiency from voltage conversions and such (a capcitor's voltage is proportional to the square root of it's stored energy, while a battery's voltage is a much flatter function of stored energy), but theoretically, yes you can do just that. The biggest issue is that capacitors typically have much lower energy densities than batteries.