Yes. You would also have to redesign the case to provide enough insulation, a typical DMM has a very different case from an oscilloscope. Look at the Tektronix TPS2000 series or the Fluke ScopeMeters. Expect degraded performance and a much higher price. Oscilloscopes have the added complication of orders of magnitude more bandwidth and multiple channels, so you have to isolate each channel. This is usually accomplished with a combination of optical and magnetic coupling, to cover the full range from DC to 100 MHz or so.
Does your battery powered scope have insulated BNC connectors, insulated probes (as shipped with Fluke ScopeMeters, I believe they are built by MC/HCK) and a proper insulated case designed to withstand mains voltages? Otherwise I would advise against using it for anything other than SELV, ie. low voltage, low power circuits.