Why would 2005 Cobalt lose steering and brakes but accelerate

steering issues possibly down to a malfunctioning power steering pump, brakes possibly down to a faulty servo or master cylinder, check for oil around the pedal, also check for oil around the steering rack and power steering pump, you can also check the reservoir (of both components) if they are empty this will indicate a leak

But why would they all happen at the same time? Dealership indicated it might be electrical. Is that possible?

could not tell you! this car may have electric power steering, take it back and ask them to plug it in to the diagnostics if fault codes come up this will indicate an electrical problem, otherwise again do visual checks around the various parts for leaks